# Hotmath Practice Problems

Title:
Hotmath Algebra 2
Author:
Hotmath Team
Chapter:Polynomial FunctionsSection:Polynomial Division, The Remainder and Factor Theorems

Problem: 1

Divide the expression.

Problem: 3

Divide the expression.

Problem: 5

Divide the expression.

Problem: 7

Divide the expression.

Problem: 9

Divide the expression.

Problem: 11

Divide the expression.

Problem: 13

Divide the expression.

Problem: 15

Simplify the expression.

Problem: 17

Simplify the expression.

Problem: 19

Simplify the expression.

Problem: 21

Divide using polynomial long division.

(x2 + 7x – 5) (x – 12)

Problem: 23

Divide using polynomial long division.

(4x4 + 9) (x2 – 1)

Problem: 25

Divide.

Problem: 27

Divide.

Problem: 29

Divide.

Problem: 31

Perform he division.

Problem: 33

Divide.

Problem: 35

Divide using synthetic division:

(x3 – 5x – 6) (x – 2)

Problem: 37

Divide using synthetic division:

(3x2 + 7x – 3) (x + 2)

Problem: 39

Perform synthetic division.

Problem: 41

Perform synthetic division.

Problem: 43

Perform synthetic division.

Problem: 45

Perform synthetic division.

Problem: 47

Find the remainder of the polynomial using synthetic division:

Problem: 49

Find the remainder of the polynomial using synthetic division:

Problem: 51

Evaluate the function using the remainder theorem:

f(x) = x2 + 3x + 7 at x = – 4

Problem: 53

Evaluate the function using the remainder theorem:

f(x) = 2x2 – 3x + x + 2 at x = 2

Problem: 55

Use synthetic substitution to find f(1) and f(–2) for a function.

f(x) = 2x2 –7x + 5

Problem: 57

Use synthetic substitution to find f(2) and f(–1) for a function.

f(x) = x3 – 12x2 – 4x + 3

Problem: 59

Factor the polynomial given that f(k) = 0.

f(x) = x3 – 6x2 – 7x + 60, k = – 3

Problem: 61

Factor the polynomial given that f(k) = 0.

f(x) = x3 – 16x2 + 43x + 60, k = 12

Problem: 63

Factor the polynomial given that f(k) = 0.

f(x) = x3 – 2x2 – 32x + 96, k = – 6

Problem: 65

One of the zeroes of the function f(x) = x3x2 – 12x is at x = –3. Determine the other zeroes.

Problem: 67

Given a polynomial and one of its factors, find the remaining factors of the polynomial.

81x5 – 243x4 – 256x + 768, x – 3

Problem: 69

Given one zero of the polynomial function, determine the other zeros.

f(x) = 7x3 + 15x2 – 19x – 3, –3

Problem: 71

Given one zero of the polynomial function, determine the other zeros.

f(x) = 3x3 + 7x2 – 43x – 15, 3

Problem: 73

Find polynomial Q(x) and constant R in 2x3 + 3x2 + 1 = Q(x)(x + 2) + R.

Problem: 75

Find polynomial Q(z) and constant R in 2z3 – 3z2 + 2z – 1 = Q(z)(z+ i) + R.

Problem: 77

You are given an expression for the volume of the rectangular prism. Determine an expression for the missing dimension.

V = 4x3 + 5x2 – 32x – 33 and the dimensions are (x + 1) and (x + 3).