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

Mar 8, 2016

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:

$y = {x}^{2} \left(x - 2\right) + 1 \left(x - 2\right)$

You can make the two x- 2 into one.

$y = \left({x}^{2} + 1\right) \left(x - 2\right)$

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: $2 x + 4 {x}^{2} - 3 x + 6 {x}^{2}$

$2 x \left(1 + 2 x\right) - 3 x \left(1 - 2 x\right)$

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

Practice exercises:

1. Factor the following polynomials, if possible:

a ) $3 {x}^{3} + 9 {x}^{2} - 2 {x}^{2} - 6 x$

b) ${x}^{8} - {x}^{3} + {x}^{7} - {x}^{2}$

c). $2 x y + 8 {x}^{2} {y}^{3} - 4 x {y}^{5} - 16 {x}^{2} {y}^{15}$

Good luck, and hello from Esquimalt!