3.5 Dividing Polynomials
Chapter
Chapter 3
Section
3.5
Solutions 51 Videos

Divide x^4 -16x^3 + 4x^2 + 10x -11 by x - 2.

1.32mins
Q1ai

Divide x^4 -16x^3 + 4x^2 + 10x -11 by x +4.

1.37mins
Q1aii

Divide x^4 -16x^3 + 4x^2 + 10x -11 by x -1.

1.06mins
Q1aiii

Are any of the binomials below factors of x^4 -16x^3 +4x^2 +10x -11? Explain.

• x- 2
• x+ 4
• x-1
0.24mins
Q1b

State the degree of the quotient for each of the following division statements, if possible.

(x^4 - 15x^3 + 2x^2 + 12x -10) \div (x^2 -4)

0.16mins
Q2a

State the degree of the quotient for each of the following division statements, if possible.

(5x^3 -4x^2 + 3x -4) \div ( x +3)

0.16mins
Q2b

State the degree of the quotient for each of the following division statements, if possible.

(x^4 - 7x^3 + 2x^2 + 9x)\div (x^3 -x^2 + 2x + 1)

0.22mins
Q2c

State the degree of the quotient for each of the following division statements, if possible.

(2x^2 +5x -4)\div (x^4 + 3x^3 - 5x^2 +4x - 2)

0.20mins
Q2d

Complete the divisions

(x^4 -15x^3 + 2x^3 + 12x -10) \div (x^2 -4)

1.22mins
Q3a

Complete the divisions

(5x^3 -4x^2 + 3x -4) \div ( x +3)

0.56mins
Q3b

Complete the divisions

(x^4 - 7x^3 + 2x^2 + 9x)\div (x^3 -x^2 + 2x + 1)

1.04mins
Q3c

Is this expression solvable? Explain.

(2x^2 +5x -4)\div (x^4 + 3x^3 - 5x^2 +4x - 2)

0.25mins
Q3d

Complete the following table.

a) Given P(x) = 2x^3 -5x^2 + 8x + 4, D(x) = x+ 3, Q(x) =2x^2 -11x + 41, find R(x).

b) Given D(x) = 2x + 4, Q(x) =3x^2 -5x + 8, R(x) = -3, find P(x).

c) Given P(x) = 6x^4 + 2x^3 + 3x^2 -11x - 9, Q(x) =2x^3 + x -4, R(x) = -5, find D(x).

a) Given P(x) = 3x^3 + x^2 -6x + 16, D(x) = x +2, R(x) =8, find Q(x).

4.09mins
Q4

Calculate each of the following using long division.

(x^3 - 2x + 1)\div (x - 4)

1.09mins
Q5a

Calculate each of the following using long division.

(x^3 + 2x^2 - 6x + 1) \div ( x +2)

0.34mins
Q5b

Calculate each of the following using long division.

(2x^3 + 5x^2 - 4x -5)\div (2x + 1)

0.43mins
Q5c

Calculate each of the following using long division.

(x^4 + 3x^3 - 2x^2 + 5x - 1)\div (x^2 + 7)

1.13mins
Q5d

Calculate each of the following using long division.

(x^4 + 6x^3 - 8x +12)\div (x^3 -x^2 -x + 1)

1.15mins
Q5e

Calculate each of the following using synthetic division.

(x^3 -7x - 6)\div(x - 3)

0.38mins
Q6a

Calculate each of the following using synthetic division.

(2x^3 - 7x^2 -7x + 19)\div(x - 1)

0.35mins
Q6b

Calculate each of the following using synthetic division.

(6x^4 + 13x^3 - 34x^2 - 47x + 28)\div(x + 3)

0.45mins
Q6c

Calculate each of the following using synthetic division.

(2x^3 +x^2 -22x + 20)\div(2x -3)

2.14mins
Q6d

Calculate each of the following using synthetic division.

(12x^4 - 56x^3 + 59x^2 + 9x -18)\div(2x + 1)

1.44mins
Q6e

Each divisor was divided into another polynomial, resulting in the given quotient and remainder. Find the other polynomial (the dividend).

divisor: x+ 10, quotient: x^2 - 6x + 9, remainder: -1

0.30mins
Q7a

Each divisor was divided into another polynomial, resulting in the given quotient and remainder. Find the other polynomial (the dividend).

divisor: 5x + 2, quotient: x^3 + 4x^2 -5x + 6, remainder: x - 2

0.29mins
Q7c

Determine the remainder, r, to make each multiplication statement true.

(2x -3)(3x +5) + r = 6x^2 +x + 5

0.42mins
Q8a

Determine the remainder, r, to make each multiplication statement true.

(x+ 3)(x +5) + r = x^2 + 9x - 7

0.46mins
Q8b

Determine the remainder, r, to make each multiplication statement true.

(x+ 3)(x^2 - 1) + r =x^3 + 3x^2 -x - 3

0.38mins
Q8c

Determine the remainder, r, to make each multiplication statement true.

(x^2 + 1)(2x^3 -1) + r = 2x^5 + 2x^3 + x^2 + 1

1.12mins
Q8d

Each dividend was divided by another polynomial, resulting in the given quotient and remainder. Find the other polynomial (the divisor).

Dividend: 5x^3 + x^2 +3, quotient: 5x^2 -14x + 42, remainder: -124

0.47mins
Q9a

Each dividend was divided by another polynomial, resulting in the given quotient and remainder. Find the other polynomial (the divisor).

Dividend: 10x^4 -x^2 + 20x -2, quotient: 10x^3 -100x^2 + 999x - 9970, remainder: 99 698

1.46mins
Q9b

Each dividend was divided by another polynomial, resulting in the given quotient and remainder. Find the other polynomial (the divisor).

Dividend: x^4 + x^3 - 10x^2 -1, quotient: x^3 - 3x^2 + 2x - 8, remainder: 31

0.39mins
Q9c

Each dividend was divided by another polynomial, resulting in the given quotient and remainder. Find the other polynomial (the divisor).

Dividend: x^3 + x^2 + 7x - 7, quotient: x^2 + 3x +13, remainder: 19

0.31mins
Q9d

Find a binomial that is a factor of the given polynomial.

x^3 + 6x^2 -x - 30

0.22mins
Q10a

Find a binomial that is a factor of the given polynomial.

x^4 - 5x^2 +4

0.35mins
Q10b

Determine whether each binomial is a factor of the given polynomial.

x^4 - 5x^2 + 6

A. x^2-3

B. x+3

C. x+1

D. x^2+1

0.22mins
Q10c

Find a binomial that is a factor of the given polynomial.

2x^4 -x^3 -4x^2 + 2x + 1

0.29mins
Q10d

Determine whether each binomial is a factor of the given polynomial.

3x + 5, 3x^6+ 5x^5+9x^2+ 17x - 1

0.59mins
Q10e

Determine whether each binomial is a factor of the given polynomial.

5x -1, 5x^4 - x^3 + 10x -10

0.24mins
Q10f

The volume of a rectangular box is (x^3 + 6x^2 + 11x +6)cm^3 . The A box is (x + 3) cm long and  (x + 2)  cm wide. How high is the box?

0.50mins
Q11

8x^3 + 10x^2 - px -5 is divisible by 2x + 1. There is no remainder. Find the value of p.

0.54mins
Q12a

When x^6 + x^4 -2x^2 + k is divided by 1 + x^2, the remainder is  5. Find the value of k.

0.45mins
Q12b

The polynomial x^3 + px^2 -x -2, p\in \mathbb{R}, has x -1 as a factor. What is the value of p?

0.34mins
Q13

Let f(x) =x^n -1, where n is an integer and n \geq 1. Name a factor that makes f(x) always divisible by it? Explain.

0.58mins
Q14

If the divisor of a polynomial, f(x), is x - 4, then the quotient is x^2 + x -6 and the remainder is 7.

• (a) Write the division statement.
• (b) Rewrite the division statement by factoring the quotient.
• (c) Graph f(x) using your results in part b).
1.31mins
Q15

The volume of a cylindrical can is (4\pi x^3 + 28 \pi x^3 + 65 \pi x + 50\pi)cm^3. The can is (x + 2) cm high. What is the radius?

1.44mins
Q17

Divide. (x^4 + x^3y -xy^3 - y^4)\div(x^2 - y^2)

1.42mins
Q18a

Divide. (x^4 -2 x^3y + 2x^2y^2 - 2xy^3 + y^4)\div(x^2 + y^2)

1.36mins
Q18b

Find a factor for x^3 - y^3.

Is f(x) = (x + 5)q(x) + (x + 3), what is the first multiple of (x + 5) that greater than f(x).