Use polynomial long division on the following problem.

Question

Use polynomial long division to perform the indicated division. Write the polynomial in the form p(x) = d(x)q(x) + r(x).

 

(2x⁴ − 3x³ + 2x² − 2) ÷ (x² + 4)

Answer 1

Hey! Lets solve this shall we ?

So, we must find the remainder and quotient given P(x) = 2x⁴-3x³+2x²-2 and D(x) = x² + 4. We will find the remainder and quotient using long division such that

2x² - 3x - 6

x² + 4 -------------------------------------------

2x⁴ - 3x³ + 2x² - 2

-(2x⁴ +8x²)

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

-3x³ - 6x² - 2

-(-3x³ - 12x)

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

-6x² + 12x - 2

-(-6x² -24)

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

12x + 22 = R(x)

So, P(x) = D(x)*Q(x) + R(x) = (x²+4)(2x²-3x-6) + (12x+22)

I hope this helped!