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

1 Answer
Mar 8, 2016

Answer:

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!