Question

What is the remainder when 19x^2 + 15x + 12 is divided by x - 2?

Answer 1

R = 118

Explanation:

Given

Represent the polynomial with P and the divisor with D

`P = 19x^2 + 15x + 12`

`D = x -2`

Required

Determine the remainder

We start by equating the divisor to 0

i.e.

`D = 0`

`x - 2 = 0`

`x = 2`

Substitute 2 for x in the polynomial.

This gives remainder (R)

`R = 19*2^2 + 15*2 + 12`

`R = 19*4 + 15*2 + 12`

`R = 76 + 30 + 12`

`R = 118`

Hence, the remainder is 118