Factoring

[tranquil ivy]

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[ivory coral]

she hasn’t completed the factorization

[winter salmon]

Wdym

Well

Then how do I find the complex roots for

x^3 - 3x^2 + x -3

[ivory coral]

factorize it?

the substitute math teacher did the first step

and presumably someone has completed the second and found (x^2+1)(x-3)

[winter salmon]

the second of what

[winter salmon]

Ok but

How is x^2(x-3) + 1(x-3)

[ivory coral]

step of factorization

[winter salmon]

The same as

[ivory coral]

i tend to think about things in steps

[winter salmon]

(x^2 + 1)(x-3)

and not (x^2)(x-3) + (x-3)

[ivory coral]

it’s equal to this as well, but this isn’t factorized

[winter salmon]

But is my substitute incorrect

[ivory coral]

what’s your substitute?

oh, the teacher

well, she didn’t finish factoring it

[winter salmon]

She factored it into: x^2(x-3)+1(x-3) and then she simplified it as (x^2 +1)(x-3)

Is this right?

[ivory coral]

this is correct

[warm burrow]

It's just the reverse distributive property.

[winter salmon]

wdynm

can you demonstrate it

[warm burrow]

You recall the distributive property of multiplication over addition?

[winter salmon]

Yeah

[warm burrow]

Can you explain what it is?

[winter salmon]

5(2x + 2) = (10x + 10)

something lik ethat

[warm burrow]

In general, a(b + c) = ab + ac.

Thus, using the symmetric property of equality, ab + ac = a(b + c).

[winter salmon]

Ok

can you help me out with

x^3 - 5x^2 + 5x - 4

I cannot factor this

[quartz cove]

it’s not factorable.

[warm burrow]

Technically all polynomials are factorable.

[warm burrow]

Did you write it wrong?

[quartz cove]

i mean, not with “traditional methods”

just needs to use rational root theorem

[astral raptor]

what have you been taught so far
like have you heard anything like "rational root theorem" "integral root thereom" smthn like that

[slow sandal]

@winter salmon

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