Find the product.

1. x2 + 2x – 24 ANSWER 2y2 + 13y + 15 ANSWER Find the product. 1. (x + 6)(x – 4) 2. (2y + 3)( y + 5)

2. 2x2 – 3x – 2; 18in.2 ANSWER Find the product. 3. The dimensions of a rectangular print can be represented by x – 2 and 2x + 1. Write an expression that models the area of the print. What is its area if x is 4 inches?

3. Factors of 18 Sum of factors 18, 1 18 + 1 = 19 9, 2 9 + 2 = 11 Correct sum 6, 3 6 + 3 = 9 EXAMPLE 1 Factor when b and c are positive Factor x2 + 11x + 18. SOLUTION Find two positive factors of 18 whose sum is 11. Make an organized list.

4. ANSWER x2+ 11x + 18 = (x +9)(x +2) = x2 + 11x + 18 EXAMPLE 1 Factor when b and c are positive The factors 9 and 2 have a sum of 11, so they are the correct values of pand q. CHECK (x + 9)(x + 2) = x2 + 2x + 9x + 18 Multiply binomials. Simplify.

5. ANSWER (x +2)(x +1) ANSWER (a +5)(a +2) ANSWER (t +7)(t +2) for Example 1 GUIDED PRACTICE Factor the trinomial 1. x2 + 3x + 2 2. a2 + 7a + 10 3. t2 + 9t + 14.

6. Factors of 8 Sum of factors –8, –1 –8 + (–1) = –9 –4, –2 –4 + (–2) = –6 Correct sum ANSWER n2– 6n + 8 = (n –4)( n –2) EXAMPLE 2 Factor when b is negative and c is positive Factor n2 – 6n + 8. Because bis negative and cis positive, pand qmust both be negative.

7. ANSWER y2+ 2y – 15 = (y +5)( y –3) Factors of –15 Sum of factors –15, 1 –15 + 1 = –14 15, –1 15 + (–1) = 14 –5, 3 –5 + 3 = –2 5, –3 5 + (–3) = 2 Correct sum EXAMPLE 3 Factor when b is positive and c is negative Factor y2 + 2y – 15. Because cis negative, pand qmust have different signs.

8. ANSWER (t –6)( t –2) ANSWER (x –3)( x –1) for Examples 2 and 3 GUIDED PRACTICE Factor the trinomial 4. x2 – 4x + 3. 5. t2 – 8t + 12.

9. (m +5)( m –4) ANSWER ANSWER (w +8)( w –2) for Examples 2 and 3 GUIDED PRACTICE Factor the trinomial 6. m2 + m – 20. 7. w2 + 6w – 16.

10. The solutions of the equation are – 6 and 3. ANSWER EXAMPLE 4 Solve a polynomial equation Solve the equation x2 + 3x = 18. x2 + 3x = 18 Write original equation. x2 + 3x – 18 = 0 Subtract 18 from each side. (x + 6)(x – 3) = 0 Factor left side. or x + 6 = 0 x – 3 = 0 Zero-product property or x = – 6 x = 3 Solve for x.

11. The solutions of the equation are – 4 and 6. ANSWER EXAMPLE 4 for Example 4 Solve a polynomial equation GUIDED PRACTICE 8. Solve the equation s2 – 2s = 24.

12. EXAMPLE 5 Solve a multi-step problem BANNER DIMENSIONS You are making banners to hang during school spirit week. Each banner requires 16.5 square feet of felt and will be cut as shown. Find the width of one banner. SOLUTION STEP 1 Draw a diagram of two banners together.

13. A= lw 33=(4+ w+ 4)w The banner cannot have a negative width, so the width is 3 feet. ANSWER EXAMPLE 5 Solve a polynomial equation STEP 2 Write an equation using the fact that the area of 2 banners is 2(16.5) = 33 square feet. Solve the equation for w. Formula for area of a rectangle Substitute 33 for Aand (4 +w + 4) for l. 0 = w2 + 8w – 33 Simplify and subtract 33 from each side. 0 = (w + 11)(w – 3) Factor right side. or w – 3 = 0 w + 11 = 0 Zero-product property w = – 11 or w = 3 Solve for w.

14. 9. WHAT IF? In example 5, suppose the area of a banner is to be 10 square feet. What is the width of one banner? 2 feet ANSWER for Example 5 GUIDED PRACTICE

15. (x +2)(x – 8) ANSWER (y +3)(y + 8) ANSWER ANSWER (x +4)(x – 3) Daily Homework Quiz Factor the trinomial. 1. x2 – 6x – 16 2. y2 + 11y + 24 3. x2 + x – 12

16. – 4, 5 ANSWER 5. Each wooden slat on a set of blinds has width w and length w + 17. The area of one slat is 38 square inches. What are the dimensions of a slat? ANSWER 2 in. by 19 in. Daily Homework Quiz 4. Solvea2 – a = 20