Question

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder.

p(x) = x⁴ – 5x + 6, g(x) = 2 – x²

Answer 1

Given polynomials are 

p(x) = x⁴ – 5x + 6 and 

g(x) = 2 – x² 

Here, the dividend is already in the standard form and the divisor is not in the standard form. 

It can be written as -x² + 2.

So, we have

∴ The quotient is -x² – 2 and the remainder is -5x + 10.