Problem 14 college algebra Please show your work Use synthet

Problem 14 (college algebra). Please show your work.

Use synthetic division to find the quotient and remainder when 9x^6 - 4x^4 + 4x^2 + 4 is divided by x-2 Quotient: Remainder:

Solution

First we have to complete the polynomial with cero and then divided

9x⁶ + 0x⁵ - 4x⁴ + 0x³ + 4x² + 0x + 4 divided x - 2

-9x⁶+ 18x⁵ -4x⁴     9x⁵+18x⁴ +32x³ + 64x²+132x+264

0 -18x⁵+36x⁴

0 32x⁴ + 0x³

-32x² +64x³

0 - 64x³+4x²

0 + 128x²+0x

132x² + 0x

-132x² +264x

   0 264x + 4   

-264x+ 528

   0+ 532

quotient =     9x⁵+18x⁴ +32x³ + 64x²+132x+264

Remainder= 532