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, 9x^4 − 35x^2 − 4(x − 2)

Answer 1

$9x^4-35x^2-4$

Lets divide this polynomial by x - 2

9x^4 0x³ -35x² 0x -4 | x - 2

-9x^4 +18x³ | 9x³

18x³ -35x² 0x -4 | x - 2

-18x³ 36x² | 9x³ + 18x²

x² 0x -4 | x - 2

-x² +2x |9x³ + 18x² + x

2x -4 |x - 2

-2x + 4 |9x³ + 18x² + x +2

0

Since there is no rest for the division, x - 2 is a factor of the given polynomial:

$9x^4-35x^2-4=(x-2)\cdot(9x^3+18x^2+x+2)$