Factoring Help

[stoic trout]

struggling to understand

[iron flax]

so for the first one

what are you stuck with

top left

[stoic trout]

I've never been shown an example of this expression with a fraction before

would it technically just be 4 or -4? I'm not sure

[iron flax]

wdym

[stoic trout]

I'm not sure, like the reciprocal of it or something but I'm just not sure how to use a fraction in this situation

[iron flax]

well if x^2 = 1/4 what is x

not considering the negative value

btw the top right one you selected is right

[stoic trout]

honestly I'm not sure how to get that

and cool bet

[iron flax]

try the different values you see for the coefficient of x

is 1/2 * 1/2 = 1/4

is 1/4 * 1/4 = 1/4

since 64 is a square we can be pretty sure to factor it like that

[stoic trout]

1/2*1/2 = 1/4
can I show u the work I have so far for it aswell?

[iron flax]

ok

so we have

(1/2x+b)^2

we know b = -8 or 8

since b^2 = 64

but since 2ab is negative

[iron flax]

which one is it?

[stoic trout]

I have m and n I think

then I'd write it like this?

[iron flax]

well we have 2ab = -8

if we know a = 1/2

what is b

[stoic trout]

-16 = b

[iron flax]

2 * 1/2 = 1

1*b = -8

then just write it in the form

(a+b)^2

and see which answer that matches

[stoic trout]

ohhhhhh this is different, I was doing a different format
oops
let me try that

the top answer?

[iron flax]

yes

now bottom left

[stoic trout]

cool ty

[iron flax]

what multiplies to ac adds to b

so ac = 90 and b = -19

so try to find the values

[stoic trout]

so am I trying to find the gcf? and turn this equation into two binomials?

[iron flax]

well 9 can be made in two ways

9 * 1 and 3 * 3

[stoic trout]

I'm not sure what two numbers can multiply and get to 90 and add to get to -19

cuz I'm trying to find m+n and m*n, no?

[iron flax]

try -9

-9 * what = 90

[stoic trout]

-10

[iron flax]

ok

[stoic trout]

OHHHH

it works it works

[iron flax]

ok

[iron flax]

since the 10 and 9 add together we want them together

[stoic trout]

I'm gonna switch the 9 and 10

[iron flax]

since if they are seperate then will multiply

[stoic trout]

there's no number besides one that can go into 9 and 10 hmm

[iron flax]

assuming the non x values are negative

if -10 * something = 10

what is that something

[stoic trout]

1

[iron flax]

mb

positive 10

[stoic trout]

-1

[iron flax]

ok and 9x * what = 9x^2

[stoic trout]

ummm

hm

just, x?

[iron flax]

yea

so we have a 9x,x,-10,-1

there is only one with those numbers

[stoic trout]

so I would just multiply them by one?

[iron flax]

which factored form has all those numbers as coefficients

[stoic trout]

or 1x

(9x-10)(x-1)

[iron flax]

yes

for the next one ac = 3 and b = 4

basically the roots multiply to 3 and add to 4

so what are they?

[stoic trout]

I'm lost 😭 sorry, I'll figure this out eventually

[iron flax]

well

[stoic trout]

I think it's the bottom answer

[iron flax]

there is only two integers that multiply to 3

no

what are they

[stoic trout]

1 and 3

[iron flax]

ok

and since x = 1

1 * 1 = 1

so coeffcients of x,x,1,3

which one is it?

[stoic trout]

(x+3)(x+1)

[iron flax]

yes

now for the last

[stoic trout]

last one is rhe same thing huh

[iron flax]

basically

since c is positive and b is negative

we can assume both numbers we are looking for are negative

so the 2 numbers multipled = 4

and they are both negative

there are only 2 integer sets for this

can you list them?

[stoic trout]

(x-4)(x-1)

[iron flax]

yea

[stoic trout]

or x,4,x,-1

[stoic trout]

cool ty!
thanks for being patient with me I appreciate your help

[iron flax]

np