factoring out the greatest common factor of

Question

Factoring out the greatest common factor of following polynomials.

                   8x⁴ - 4 x³ + 10 x²

 Solution

Primary we will notice that we can factor out a 2 out of every term.  Also note that we can factor an x² out of each term.  Here then is the factoring for this problem.

8x⁴ - 4 x³ + 10 x²  = 2 x² (4 x² - 2 x +5)

Note that always we can check our factoring through multiplying the terms back out to ensure we get the original polynomial.