Section 8.2

1 / 14

# Section 8.2 - PowerPoint PPT Presentation

Section 8.2. Factoring Using the Distributive Property. Factor polynomials by using the Distributive Property. Solve quadratic equations of the form ax 2 + bx = 0. factoring. factoring by grouping Zero Products Property roots. Factor by Using the Distributive Property.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'Section 8.2' - salome

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Section 8.2

Factoring Using the

Distributive Property

Factor polynomials by using the Distributive Property.
• Solve quadratic equations of the form ax2 + bx = 0.
• factoring
• factoring by grouping
• Zero Products Property
• roots
Factor by Using the Distributive Property

In Ch.7, you used the distributive property to multiply a polynomial

by a monomial.

2a(6a + 8) = 2a(6a) + 2a(8)

= 12a² + 16a

You can reverse this process to express a polynomial as the product

of a monomial factor and a polynomial factor.

12a² + 16a = 2a(6a) + 2a(8)

= 2a(6a + 8)

Factoring a polynomial means to find its completely factored form.

Use the Distributive Property

A. Use the Distributive Property to factor 15x + 25x2.

First, find the GCF of 15x + 25x2.

15x = 3 ● 5 ● x Factor each monomial.

25x2 = 5 ● 5 ● x ● x Circle the common prime factors.

GCF: 5 ● x or 5x

Write each term as the product of the GCF and its remaining factors. Then use the Distributive Property to factor out the GCF.

15x + 25x2 = 5x(3) + 5x(5 ● x) Rewrite each term using the GCF.

Use the Distributive Property

= 5x(3) + 5x(5x) Simplify remaining factors.

= 5x(3 + 5x) Distributive Property

12xy = 2 ● 2 ● 3 ● x ● y Factor each monomial.

24xy2 = 2 ● 2 ● 2 ● 3 ● x ● y ● y

30x2y4 = 2 ● 3 ● 5 ● x ● x● y ● y ● y ● y

Use the Distributive Property

B. Use the Distributive Property to factor 12xy + 24xy2 – 30x2y4.

Circle the common prime factors.

GCF: 2 ● 3 ● x ● y or 6xy

12xy + 24xy2 – 30x2y4 = 6xy(2) + 6xy(4y) + 6xy(–5xy3) Rewrite each term using the GCF.

Use the Distributive Property

= 6xy(2 + 4y – 5xy3) Distributive Property

Answer: The factored form of 12xy + 24xy2 – 30x2y4 is 6xy(2 + 4y – 5xy3).

or more terms is called factoring by groupingbecause pairs of terms

are grouped together and factored.

Use Grouping

Factor 2xy + 7x – 2y – 7.

2xy + 7x – 2y – 7

= (2xy – 2y) + (7x – 7) Group terms with common factors.

= 2y(x – 1) + 7(x – 1) Factor the GCF from each grouping.

= (x – 1)(2y + 7) Distributive Property

Answer: (x – 1)(2y + 7)

• factoring by grouping.
• For example, 7 - y and y – 7 are additive inverses.
• By rewriting 7 - yas -1(y – 7), factoring by grouping is possible

Factor 15a – 3ab + 4b – 20.

15a – 3ab + 4b – 20 = (15a – 3ab) + (4b – 20)Group terms with common factors.

= 3a(5 – b) + 4(b – 5)Factor GCF from each grouping.

= 3a(–1)(b – 5) + 4(b – 5)5 – b = –1(b – 5)

= –3a(b – 5) + 4(b – 5)3a(–1) = –3a

Answer: = (b – 5)(–3a + 4) Distributive Property

6(0) = 0 0(-3) = 0 (5 – 5)(0) = 0 -2(-3 + 3) = 0

Notice that in each case, at least one of the factors is zero.

The solutions of an equation are called the roots of the equation.

Solve an Equation

A. Solve (x – 2)(4x – 1) = 0. Check the solution.

If (x – 2)(4x – 1) = 0, then according to the Zero Product Property, either x – 2 = 0 or 4x – 1 = 0.

(x – 2)(4x – 1) = 0 Original equation

x – 2 = 0 or 4x – 1 = 0 Set each factor equal to zero.

x = 2 4x = 1 Solve each equation.

Homework Assignment #43

8.2 Skills Practice Sheet