VCE Stuff > VCE Mathematical Methods CAS

how do I factor a quadratic equation?

(1/2) > >>

annaoh_2003:
Hi everyone,

Im wanting to find x intercepts and wondering how to factor this equation. I used an algebra calculator but it didn't tell me how to factor the equation.

Thanks :)

Tapioca:
.

annaoh_2003:

--- Quote from: Tapioca on January 23, 2022, 05:10:17 pm ---Let f(x) = 2x^3 - 3x^2 -3x + 2
Because f(-1)= 0, then x+1 is a factor:

Factorise
= 2x^2(x+1) - 5x(x+1) +2(x+1)

Simplify
= (x+1)(2x^2 -5x +2)
= (x+1) (2x-1) (x-2)

Done  :)

--- End quote ---


little bit confused- how come you used -1 in f(x)? im struggling to see how you factorised and simplified it. sorry im a bit slow with maths  ;D could you explain it a bit more?

Tapioca:
.

Bri MT:

--- Quote from: annaoh_2003 on January 23, 2022, 05:18:43 pm ---
little bit confused- how come you used -1 in f(x)? im struggling to see how you factorised and simplified it. sorry im a bit slow with maths  ;D could you explain it a bit more?

--- End quote ---

I'm adding to Tapioca's explanation since it seems like you may not have covered the polynomial theorem in school yet which teaches that if f(a) = 0 then (x -a) is a factor of f(x). It's common to test easy numbers first (like 1, -1, 2, -2) when trying to find the first factor.

It might be easiest to first see this looking from the other perspective.
if you have (x-a)(x-c)(x-d)  then we know we can make the whole thing = 0 by making one of the brackets equal zero. (null factor law).
I.e. if (x-a) is a factor, then making x = a means that the equation equals zero.

So to restate, Tapioca was using the similar idea that if have x = a makes the whole thing equal zero, then that means (x-a) is a factor.

That's the first step.  The 2nd step may also be a bit tricky but before we move on I think it's important to check that you get the first one :)


Kudos to you for reaching out for help and to Tapioca for the explanations :)

Navigation

[0] Message Index

[#] Next page