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

1 Answer
Noah G
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(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!

Related questions
See all questions in Monomial Factors of Polynomials
Impact of this question
1449 views around the world
You can reuse this answer
Creative Commons License