Related Topics:

Lesson Plans and Worksheets for Algebra I

Lesson Plans and Worksheets for all Grades

More Lessons for Algebra I

Common Core For Algebra I

Examples, videos, and solutions to help Algebra I students learn how to solve equations involving factored expressions.

Worksheets for Algebra I, Module 1, Lesson 17 (Teacher Version)

Worksheets for Algebra I, Module 1, Lesson 17 (Student Version)

Lesson 17 Student Outcomes

Students learn that equations of the form (x - a)(x - b) = 0 have the same solution set as two equations joined by βorβ: x - a = 0 or x - b = 0.

Students solve factored or easily factorable equations.

Lesson 17 Summary

The zero-product property says that If ab = 0, then either a = 0 or b = 0 or a = b = 0.

Exercise 1

- Solve each equation for π₯.

a. π₯ β 10 = 0

b. π₯^{2}+ 20 = 0

c. Demanding Dwight insists that you give him two solutions to the following equation:

(π₯ β 10)(π₯^{2}+ 20) = 0

Can you provide him with two solutions?

d. Demanding Dwight now wants FIVE solutions to the following equation:

(π₯ β 10)(2π₯ + 6)(π₯^{2}β36)(π₯^{2}+ 10)(π₯/2 + 20) = 0

Can you provide him with five solutions?

Do you think there might be a sixth solution?

Consider the equation (π₯ β4)(π₯ + 3) = 0.

e. Rewrite the equation as a compound statement.

f. Find the two solutions to the equation.

Example 1

Solve 2π₯^{2} β 10π₯ = 0, for π₯.

Example 2

Solve π₯(π₯ β 3)+ 5(π₯ β 3) = 0, for π₯.

Exercises 2β7

2. (π₯ + 1)(π₯ + 2) = 0

3. (3π₯ β 2)(π₯ + 12) = 0

4. (π₯ β 3)(π₯ β 3) = 0

5. (π₯ + 4)(π₯ β 6)(π₯ β 10) = 0

6. π₯^{2} β 6π₯ = 0

7. π₯(π₯ β 5)+ 4(π₯ β 5) = 0

Example 3

Consider the equation (π₯ β2)(2π₯ β 3) = (π₯ β 2)(π₯ +5). Lulu chooses to multiply through by
1/π₯β2 and gets the answer π₯ = 8. But Poindexter points out that π₯ = 2 is also an answer, which Lulu missed.

a. Whatβs the problem with Luluβs approach?

b. Use factoring to solve the original equation for π₯.

Exercises 8β11

8. Use factoring to solve the equation for π₯: (π₯ β 2)(2π₯ β 3) = (π₯ β 2)(π₯ + 1).

9. Solve each of the following for π₯:

a. π₯ + 2 = 5

b. π₯^{2} + 2π₯ = 5π₯

c. π₯(5π₯ β 20)+ 2(5π₯ β 20) = 5(5π₯ β 20)

10. a. Verify: (π β 5)(π + 5) = π^{2} β25.

b. Verify: (π₯ β 88)(π₯ + 88) = π₯^{2} β 88^{2}

c. Verify: π΄^{2} β π΅^{2} = (π΄ β π΅)(π΄ + π΅).

d. Solve for π₯: π₯^{2} β 9 = 5(π₯ β 3).

e. Solve for π€: (π€ + 2)(π€ β 5) = π€^{2} β 4.

11. A string 60 inches long is to be laid out on a tabletop to make a rectangle of perimeter 60 inches. Write the width of
the rectangle as 15 + π₯ inches. What is an expression for its length? What is an expression for its area? What value
for π₯ gives an area of the largest possible value? Describe the shape of the rectangle for this special value of π₯.

Exit Ticket

- Find the solution set to the equation 3x
^{2}+ 27x = 0 - Determine if each statement is true or false. If the statement is false, explain why or show work proving that it is false.

a. If a = 5 then ac = 5c

b. If ac = 5c then a = 5

Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.