# Math Questions With Answers (9): Polynomial Division

More Math questions on synthetic division of polynomials are presented. Answers to these questions are located at the lower part of the page.

## Question 1

Use synthetic division to find the quotient Q and remainder R when dividing the polynomial
2x
2 + x by x - 1.

## Question 2

Use synthetic division to find the quotient Q and remainder R when dividing the polynomial
4x
3 + x2 - 2x + 3 by x + 2.

## Question 3

Use synthetic division to find the quotient Q and remainder R when dividing the polynomial
7x
5 - 2x4 - 5x3 + x2 - 3x + 5 by x - 2.

## Question 4

Use synthetic division to find the quotient Q and remainder R when dividing the polynomial
(1/2)x
3 - (1/3)x2 - (3/2) x + 1/3 by x - 1/2.

## Question 5

Use synthetic division to find the quotient Q and remainder R when dividing the polynomial
0.3 x
3 - 0.2x2 - 0.1 x + 0.3 by x - 0.2.

## Question 6

Use synthetic division and the remainder theorem to determine f(-2) given that f(x) = 5x4 - 4x3 - x2 + 5

## Question 7

Use synthetic division and the remainder theorem to determine f(1/2) given that f(x) = -3x5 + x3 - 2x2 + x - 3

## Question 8

Use synthetic division and the remainder theorem to determine f(0.2) given that f(x) = 0.1 x3 - 0.6x2 - 0.6

## Question 9

Use synthetic division to find the quotient Q and remainder R when dividing f(x) = x2 + 2x + 3 by x - i. (i = √(-1) the imaginary unit)

## Question 10

Use synthetic division to find the quotient Q and remainder R when dividing f(x) = x5 + x4 + x3 +2x - 5 by x + i. (i = √(-1) the imaginary unit)

1) Q = 2x + 3 , R = 3
2) Q = 4x2 - 7x + 12 , R = -21
3) Q = 7x4 + 12x3 + 19x2 + 39x + 75, R = 155
4) Q = (1/2)x2 - (1/2)x - 37/24 , R = -7/16
5) 0.3 x2 - 0.14 x - 0.128 , R = 0.2744
6) 113
7) 95/32
8) -0.6232
9) Q = x + 2 + i , R = 2 + 2i
10) Q = x4 + (1 - i) x3 - ix2 - x + 2 + i , R = -2i - 4