Lesson: Dividing a Polynomial by a Binomial Using Factorization

In this lesson, we will learn how to divide polynomials by polynomials using factorization and how to find common factors that will cancel out.

Sample Question Videos

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Worksheet: Dividing a Polynomial by a Binomial Using Factorization • 15 Questions • 3 Videos

Q1:

Find the value of 𝑘 that makes the expression 𝑥 𝑘 𝑥 + 3 0 2 divisible by 𝑥 5 .

Q2:

The area of a triangle is 1 2 𝑥 + 3 8 𝑥 + 2 8 2 cm2 and its base is ( 2 𝑥 + 4 ) cm. Write an expression for its height.

Q3:

What is the width of a rectangle whose area is 4 𝑥 3 2 𝑥 + 6 𝑥 3 2 4 cm2 and whose length is 8 𝑥 + 3 𝑥 2 cm?

Q4:

By factoring, find all the solutions to 𝑥 𝑥 1 4 𝑥 + 2 4 = 0 3 2 , given that ( 𝑥 + 4 ) is a factor of 𝑥 𝑥 1 4 𝑥 + 2 4 3 2 .

Q5:

A rectangle has an area of 𝑦 + 2 𝑦 + 5 𝑦 + 1 0 3 2 cm2 and a width of ( 𝑦 + 2 ) cm. Find its length in terms of 𝑦 and its perimeter when 𝑦 = 4 .

Q6:

Knowing that the length of a rectangle is 2 𝑥 + 5 and its area is 4 𝑥 + 1 0 𝑥 + 6 𝑥 + 1 5 3 2 , express the width of the rectangle algebraically.

Q7:

Knowing that the volume of a box is 1 0 𝑥 + 3 0 𝑥 8 𝑥 2 4 3 2 , its length is 2, and its width is 𝑥 + 3 , express the height of the box algebraically.

Q8:

+ 5 0 𝑎 𝑏 + 3 8 𝑎 𝑏 = 2 1 𝑎 𝑏 + 2 5 𝑏 + 1 9 2 .

Q9:

Find the value of 𝑘 that makes the expression 𝑥 𝑘 𝑥 + 2 0 2 divisible by 𝑥 5 .

Q10:

Find the value of 𝑘 that makes the expression 𝑥 𝑘 𝑥 1 8 2 divisible by 𝑥 + 2 .

Q11:

The area of a triangle is 1 8 𝑥 + 7 3 𝑥 + 3 5 2 cm2 and its base is ( 2 𝑥 + 7 ) cm. Write an expression for its height.

Q12:

The area of a triangle is 4 8 𝑥 + 6 2 𝑥 + 9 2 cm2 and its base is ( 8 𝑥 + 9 ) cm. Write an expression for its height.

Q13:

What is the width of a rectangle whose area is 1 4 𝑥 + 7 2 𝑥 8 𝑥 4 2 6 cm2 and whose length is 8 𝑥 2 𝑥 3 cm?

Q14:

What is the width of a rectangle whose area is 5 9 𝑥 3 6 𝑥 + 7 𝑥 5 4 6 cm2 and whose length is 9 𝑥 + 𝑥 2 3 cm?

Q15:

A rectangle has an area of 𝑦 + 1 0 𝑦 + 7 𝑦 + 7 0 3 2 cm2 and a width of ( 𝑦 + 1 0 ) cm. Find its length in terms of 𝑦 and its perimeter when 𝑦 = 2 .

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