Dividing polynomials by monomials

This section will teach us how to divide a polynomial (more than one term) by a monomial (one term only). We will use a model to help us on the division. We will then try to solve the questions without using the model. At the end, we will look at some of the related word problems.

Basic concepts:
Understanding integer division
Equivalent expressions of polynomials
Multiplying and dividing monomials
Multiplying polynomials by monomials

Related concepts:
Multiplying monomial by monomial
Multiplying monomial by binomial
Multiplying binomial by binomial
Multiplying polynomial by polynomial

Lessons

- a)
  How to divide polynomials by monomials?
2.
Divide by using a model.
3.
Divide.
4.
The volume of the diagram below is $45{x^2} + 3x$ .

Dividing polynomials by monomials

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Basic MathUnderstanding integer division

AlgebraEquivalent expressions of polynomials

AlgebraMultiplying and dividing monomials

AlgebraMultiplying polynomials by monomials

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Understanding integer division

Equivalent expressions of polynomials

Multiplying and dividing monomials

Multiplying polynomials by monomials

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Lesson: 2a

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Lesson: 3c

Lesson: 3d

Lesson: 4a

Lesson: 4b

Intro

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Don't just watch, practice makes perfect.

Do better in math today

Don't just watch, practice makes perfect.

Lessons

1.

a)

How to divide polynomials by monomials?

2.

Divide by using a model.

a)

6x2−24x3x\frac{{6{x^2} - 24x}}{{3x}}​3x​​6x​2​​−24x​​

b)

−5x2−7x−x\frac{{ - 5{x^2} - 7x}}{{ - x}}​−x​​−5x​2​​−7x​​

3.

Divide.

a)

4x2+12xy2x\frac{{4{x^2} + 12xy}}{{2x}}​2x​​4x​2​​+12xy​​

b)

3.5x2+2.1x7x\frac{{3.5{x^2} + 2.1x}}{{7x}}​7x​​3.5x​2​​+2.1x​​

c)

−x2−1.8xy6x\frac{{ - {x^2} - 1.8xy}}{{6x}}​6x​​−x​2​​−1.8xy​​

d)

−18x2−9x+0.30.3\frac{{ - 18{x^2} - 9x + 0.3}}{{0.3}}​0.3​​−18x​2​​−9x+0.3​​

4.

The volume of the diagram below is 45x2+3x45{x^2} + 3x45x​2​​+3x.

a)

Write the polynomial expression for the width of the diagram.

b)

If x = 3 m, calculate the width and the volume.

Don't just watch, practice makes perfect.

Dividing polynomials by monomials

Don't just watch, practice makes perfect.

We have over 1130 practice questions in Basic Algebra for you to master.

Basic Math
Understanding integer division

Algebra
Equivalent expressions of polynomials

Algebra
Multiplying and dividing monomials

Algebra
Multiplying polynomials by monomials

or

$\frac{{6{x^2} - 24x}}{{3x}}$

$\frac{{ - 5{x^2} - 7x}}{{ - x}}$

$\frac{{4{x^2} + 12xy}}{{2x}}$

$\frac{{3.5{x^2} + 2.1x}}{{7x}}$

$\frac{{ - {x^2} - 1.8xy}}{{6x}}$

$\frac{{ - 18{x^2} - 9x + 0.3}}{{0.3}}$

The volume of the diagram below is $45{x^2} + 3x$ .