Question

Use synthetic division to determine whether the first expression is a factor of the second. If it is, indicate the factorization. (If the first expression is not a factor of the second, enter DNE.)x − 2, 3x4 − 6x3 − 8x + 16(x − 2)=

Answer 1

Find out the division

3x^4-6x^3-8x+16 : (x-2)

3x^3-8

-3x^4+6x^3

-----------------------

-8x+16

8x-16

------------

0

The remainder is zero

that means

The expression (x-2) is a factor of the polynomial

so

3x^4-6x^3-8x+16=(x-2)(3x^3-8)