Solving polynomial functions algebraically | Mathematics | Page 1

molten hinge Oct 12, 2024, 9:09 AM

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I need help with this, and it's explanation, I got an exam on wednesday frfr

eager talonBOT Oct 12, 2024, 9:10 AM

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molten hinge I need help with this, and it's explanation, I got an exam on wednesday frfr

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molten hinge Oct 12, 2024, 9:10 AM

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despair

charred pivot Oct 12, 2024, 9:10 AM

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any specific example?

molten hinge Oct 12, 2024, 9:12 AM

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this I guess

charred pivot Oct 12, 2024, 9:12 AM

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you can't really solve for that; it's not an equation

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did you mean factor?

molten hinge Oct 12, 2024, 9:13 AM

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It says on my book module 3, solving polynomial equations algebraically

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Ill give u a question

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the teacher gave us then

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cuz this is from youtube

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4x^3 + 12x^2 - 9x - 27 = 0

charred pivot Oct 12, 2024, 9:15 AM

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try to factor it

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this one can be grouped

molten hinge Oct 12, 2024, 9:16 AM

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that question is solved, but I wrote down what he wrote, so ill type how this was presented to me

willow needle Oct 12, 2024, 9:16 AM

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molten hinge 4x^3 + 12x^2 - 9x - 27 = 0

if you can get into a form like a(b+c) + d(b+c) = 0, it can be grouped into pairs --> (b+c)(a+d) = 0

molten hinge Oct 12, 2024, 9:16 AM

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cuz i didnt understand it

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js fixed one thing

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its, cubed not squared

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mb fr

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the teacher paired it

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and he wrote

charred pivot Oct 12, 2024, 9:17 AM

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molten hinge the teacher paired it

as he should

molten hinge Oct 12, 2024, 9:17 AM

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(4x^3+12x^2) + (-9x-27) = 0

charred pivot Oct 12, 2024, 9:18 AM

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you made a typo

molten hinge Oct 12, 2024, 9:18 AM

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?

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that

charred pivot Oct 12, 2024, 9:18 AM

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fixed

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yes

molten hinge Oct 12, 2024, 9:18 AM

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okay

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from what i recall he said pick the lower exponent/power from the two

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which was

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^2

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and he he simplified the whole equation even smaller

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and smaller, it was confusing to me tbh

charred pivot Oct 12, 2024, 9:20 AM

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what?

molten hinge Oct 12, 2024, 9:20 AM

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let me show ya

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my handwriting is insane LOL mb mb, I was writing fast

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this i did NOT understand

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he said pair it first, and he showed it

charred pivot Oct 12, 2024, 9:22 AM

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hm ok

molten hinge Oct 12, 2024, 9:23 AM

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then he said from between the 4 and 12, pick the lower power

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which was ^2

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and then i got thrown off

charred pivot Oct 12, 2024, 9:23 AM

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we are trying to factor each pair

molten hinge Oct 12, 2024, 9:23 AM

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when he showed me how to get the 4

molten hinge Oct 12, 2024, 9:23 AM

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charred pivot we are trying to factor each pair

I see

charred pivot Oct 12, 2024, 9:23 AM

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charred pivot we are trying to factor each pair

for example, start with (4x^3+12x^2)

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and pick out every common factor from it

molten hinge Oct 12, 2024, 9:24 AM

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mhm

charred pivot Oct 12, 2024, 9:24 AM

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the 4 comes from being a factor of 4 and 12 both

molten hinge Oct 12, 2024, 9:25 AM

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uhuh

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Wait

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How would I get the factors exactly?

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Wait

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He said 2 divided by 12 is 6 and 2 divided by 4 is 2 and he kept dividing

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Until 12 became 3 and 4 became 1

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And he stopped dividing them

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Are those the factors ?

charred pivot Oct 12, 2024, 9:32 AM

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2 and 2, yes

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(2*2=4)

molten hinge Oct 12, 2024, 9:32 AM

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the 2 and 2 r factors, correct?

charred pivot Oct 12, 2024, 9:33 AM

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yes, so you can take them out

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4(x^3 + 3x^2)

molten hinge Oct 12, 2024, 9:34 AM

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wait

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so u

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kept dividing the

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4 into 1

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and it became x? since x is 1

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while 12 became 3 after dividing it those many times

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how do you know when to stop dividing

charred pivot Oct 12, 2024, 9:35 AM

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1 and 3 don't have any common factors

molten hinge Oct 12, 2024, 9:38 AM

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for a factor there has to be no remainder when dividing correct

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?

charred pivot Oct 12, 2024, 9:38 AM

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yes

charred pivot Oct 12, 2024, 9:39 AM

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charred pivot 1 and 3 don't have any common factors

1 doesn't count because 1*anything = itself

molten hinge Oct 12, 2024, 9:41 AM

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I see, so 4, would be 4 2 and 1

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I understand, im js tryna solidify it

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that removes, hella confusion

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teacher confused the hell out of me

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in this case, it would be, 1, 2, 5, 10

charred pivot Oct 12, 2024, 9:44 AM

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if both of the numbers are divisible by 10, sure

molten hinge Oct 12, 2024, 9:44 AM

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I see, alright then

charred pivot Oct 12, 2024, 9:44 AM

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molten hinge in this case, it would be, 1, 2, 5, 10

generally we will seek to take the greatest common factor out

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for example, here, it is 10

charred pivot Oct 12, 2024, 9:45 AM

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charred pivot if both of the numbers are divisible by 10, sure

(edited)

molten hinge Oct 12, 2024, 9:46 AM

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So we picked 4, because its the factor of both, and its the greatest common factor

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alright ty

molten hinge Oct 12, 2024, 9:46 AM

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charred pivot 4(x^3 + 3x^2)

u can continue

charred pivot Oct 12, 2024, 9:46 AM

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now you have to take out the powers of x

molten hinge Oct 12, 2024, 9:51 AM

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how so?

molten hinge Oct 12, 2024, 10:13 AM

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_thinccat

charred pivot Oct 12, 2024, 10:18 AM

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consider the largest power of x dividing both x^3 and 3x^2

molten hinge Oct 12, 2024, 10:21 AM

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the factor is 4, its the greatest factor

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and between the two powers

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the lower is 2

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and so u use that

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which becomes 4^2

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correct?

charred pivot Oct 12, 2024, 10:23 AM

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4x^2

molten hinge Oct 12, 2024, 10:27 AM

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right right

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forgot the x

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okay. and the number that cant be divided anymore

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is 1 and 3

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so its x and 3

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making it 4x^2(x+3)

charred pivot Oct 12, 2024, 10:28 AM

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4x^2(x+3)

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now do the same with the other one

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(-9x-27)

molten hinge Oct 12, 2024, 10:28 AM

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the greatest factor between the two is -9

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the least 27 can get to is 3, and 9 is 1, right?

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ignore da plus and minus, i mean js number wise

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is that correct?

charred pivot Oct 12, 2024, 10:31 AM

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yes

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and it's common practice to take the - out

molten hinge Oct 12, 2024, 10:35 AM

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-9(x+3)?

charred pivot Oct 12, 2024, 10:35 AM

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yes

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so you have 4x^2(x+3) - 9(x+3)

molten hinge Oct 12, 2024, 11:00 AM

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Okay, what’s the next step?

austere willow Oct 12, 2024, 12:38 PM

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molten hinge Okay, what’s the next step?

factor out (x+3)

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so we have (4x^2-9)(x+3)

molten hinge Oct 12, 2024, 2:02 PM

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austere willow so we have (4x^2-9)(x+3)

so u js take the two numbers out of the equations and put em together, and u take the common pair which is x+3 and u put it aside

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and das it

austere willow Oct 12, 2024, 2:03 PM

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molten hinge so u js take the two numbers out of the equations and put em together, and u tak...

👍

molten hinge Oct 16, 2024, 2:37 PM

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charred pivot so you have 4x^2(x+3) - 9(x+3)

I aced the exam

molten hinge Oct 16, 2024, 2:37 PM

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austere willow 👍

I aced the exam

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tyall both

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Lol

austere willow Oct 16, 2024, 3:51 PM

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yw

charred pivot Oct 16, 2024, 8:52 PM

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nice

latent nymphBOT Nov 7, 2024, 6:03 PM

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@molten hinge

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indigo crystal Nov 7, 2024, 7:00 PM

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+close

#Solving polynomial functions algebraically