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Lesson Plans and Worksheets for Algebra I

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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.

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

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