Question

How do you factor `y= x^3-2x^2+x-2` ?

Answer 1

For polynomials like this one, you must find a number to factor out by grouping

Explanation:

The GCF (greatest common factor) of the first two is `x^2`. The GCF of the last two is 1. So, we get:

`y = x^2(x - 2) + 1(x - 2)`

You can make the two x- 2 into one.

`y = (x^2 + 1)(x - 2)`

If you distribute you'll get the same thing as at the beginning. Beware: this method only works if the two expressions are the same (x - 2 in your problem)

Example: `2x + 4x^2 - 3x + 6x^2`

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

As you can see, we can't go further because we have `1 + 2x` and `1 - 2x`.

Practice exercises:

1. Factor the following polynomials, if possible:

a ) `3x^3 + 9x^2 - 2x^2 - 6x`

b) `x^8 - x^3 + x^7 - x^2`

c). `2xy + 8x^2y^3 - 4xy^5 - 16x^2y^15`

Good luck, and hello from Esquimalt!