Warm-Up Exercises Find the product. 1.(x + 6)(x – 4) 2.(2y + 3)( y + 5) ANSWER x 2 + 2x – 24...
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Transcript of Warm-Up Exercises Find the product. 1.(x + 6)(x – 4) 2.(2y + 3)( y + 5) ANSWER x 2 + 2x – 24...
![Page 1: Warm-Up Exercises Find the product. 1.(x + 6)(x – 4) 2.(2y + 3)( y + 5) ANSWER x 2 + 2x – 24 ANSWER 2y 2 + 13y + 15.](https://reader035.fdocuments.in/reader035/viewer/2022062423/56649e6b5503460f94b68b5d/html5/thumbnails/1.jpg)
Warm-Up Exercises
Find the product.
1. (x + 6)(x – 4)
2. (2y + 3)( y + 5)
ANSWER x2 + 2x – 24
ANSWER 2y2 + 13y + 15
![Page 2: Warm-Up Exercises Find the product. 1.(x + 6)(x – 4) 2.(2y + 3)( y + 5) ANSWER x 2 + 2x – 24 ANSWER 2y 2 + 13y + 15.](https://reader035.fdocuments.in/reader035/viewer/2022062423/56649e6b5503460f94b68b5d/html5/thumbnails/2.jpg)
Warm-Up Exercises
ANSWER 2x2 – 3x – 2; 18in.2
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?
![Page 3: Warm-Up Exercises Find the product. 1.(x + 6)(x – 4) 2.(2y + 3)( y + 5) ANSWER x 2 + 2x – 24 ANSWER 2y 2 + 13y + 15.](https://reader035.fdocuments.in/reader035/viewer/2022062423/56649e6b5503460f94b68b5d/html5/thumbnails/3.jpg)
Warm-Up ExercisesFactor when b and c are positiveEXAMPLE 1
Factor x2 + 11x + 18.
SOLUTION
Find two positive factors of 18 whose sum is 11. Make an organized list.
Factors of 18 Sum of factors
18, 1
9, 2
6, 3
18 + 1 = 19
9 + 2 = 11
6 + 3 = 9
Correct sum
![Page 4: Warm-Up Exercises Find the product. 1.(x + 6)(x – 4) 2.(2y + 3)( y + 5) ANSWER x 2 + 2x – 24 ANSWER 2y 2 + 13y + 15.](https://reader035.fdocuments.in/reader035/viewer/2022062423/56649e6b5503460f94b68b5d/html5/thumbnails/4.jpg)
Warm-Up ExercisesFactor when b and c are positiveEXAMPLE 1
The factors 9 and 2 have a sum of 11, so they are the correct values of p and q.
ANSWER
x2 + 11x + 18 = (x + 9)(x + 2)
(x + 9)(x + 2) Multiply binomials.= x2 + 2x + 9x + 18
Simplify.
CHECK
= x2 + 11x + 18
![Page 5: Warm-Up Exercises Find the product. 1.(x + 6)(x – 4) 2.(2y + 3)( y + 5) ANSWER x 2 + 2x – 24 ANSWER 2y 2 + 13y + 15.](https://reader035.fdocuments.in/reader035/viewer/2022062423/56649e6b5503460f94b68b5d/html5/thumbnails/5.jpg)
Warm-Up ExercisesGUIDED PRACTICE for Example 1
Factor the trinomial
1. x2 + 3x + 2
ANSWER (x + 2)(x + 1)
2. a2 + 7a + 10
ANSWER (a + 5)(a + 2)
3. t2 + 9t + 14.
ANSWER (t + 7)(t + 2)
![Page 6: Warm-Up Exercises Find the product. 1.(x + 6)(x – 4) 2.(2y + 3)( y + 5) ANSWER x 2 + 2x – 24 ANSWER 2y 2 + 13y + 15.](https://reader035.fdocuments.in/reader035/viewer/2022062423/56649e6b5503460f94b68b5d/html5/thumbnails/6.jpg)
Warm-Up ExercisesFactor when b is negative and c is positiveEXAMPLE 2
Factor n2 – 6n + 8.
Because b is negative and c is positive, p and q must both be negative.
ANSWER
n2 – 6n + 8 = (n – 4)( n – 2)
Factors of 8 Sum of factors
–8, –1
–4, –2
–8 + (–1) = –9
–4 + (–2) = –6 Correct sum
![Page 7: Warm-Up Exercises Find the product. 1.(x + 6)(x – 4) 2.(2y + 3)( y + 5) ANSWER x 2 + 2x – 24 ANSWER 2y 2 + 13y + 15.](https://reader035.fdocuments.in/reader035/viewer/2022062423/56649e6b5503460f94b68b5d/html5/thumbnails/7.jpg)
Warm-Up ExercisesFactor when b is positive and c is negativeEXAMPLE 3
Factor y2 + 2y – 15.
Because c is negative, p and q must have different signs.
Factors of –15 Sum of factors
–15, 1
–5, 3
–15 + 1 = –14
15 + (–1) = 14
–5 + 3 = –2
15, –1
5, –3 5 + (–3) = 2 Correct sum
ANSWER y2 + 2y – 15 = (y + 5)( y – 3)
![Page 8: Warm-Up Exercises Find the product. 1.(x + 6)(x – 4) 2.(2y + 3)( y + 5) ANSWER x 2 + 2x – 24 ANSWER 2y 2 + 13y + 15.](https://reader035.fdocuments.in/reader035/viewer/2022062423/56649e6b5503460f94b68b5d/html5/thumbnails/8.jpg)
Warm-Up Exercises
4. x2 – 4x + 3.
ANSWER (x – 3)( x – 1)
GUIDED PRACTICE for Examples 2 and 3
Factor the trinomial
5. t2 – 8t + 12.
ANSWER (t – 6)( t – 2)
![Page 9: Warm-Up Exercises Find the product. 1.(x + 6)(x – 4) 2.(2y + 3)( y + 5) ANSWER x 2 + 2x – 24 ANSWER 2y 2 + 13y + 15.](https://reader035.fdocuments.in/reader035/viewer/2022062423/56649e6b5503460f94b68b5d/html5/thumbnails/9.jpg)
Warm-Up Exercises
6. m2 + m – 20.
GUIDED PRACTICE for Examples 2 and 3
Factor the trinomial
ANSWER (m + 5)( m – 4)
7. w2 + 6w – 16.
ANSWER (w + 8)( w – 2)
![Page 10: Warm-Up Exercises Find the product. 1.(x + 6)(x – 4) 2.(2y + 3)( y + 5) ANSWER x 2 + 2x – 24 ANSWER 2y 2 + 13y + 15.](https://reader035.fdocuments.in/reader035/viewer/2022062423/56649e6b5503460f94b68b5d/html5/thumbnails/10.jpg)
Warm-Up ExercisesEXAMPLE 4 Solve a polynomial equation
Solve the equation x2 + 3x = 18.
Write original equation.x2 + 3x = 18
Subtract 18 from each side.x2 + 3x – 18 = 0
Factor left side.(x + 6)(x – 3) = 0
Zero-product propertyx – 3 = 0x + 6 = 0
Solve for x.x = 3
or
orx = – 6
ANSWER The solutions of the equation are – 6 and 3.
![Page 11: Warm-Up Exercises Find the product. 1.(x + 6)(x – 4) 2.(2y + 3)( y + 5) ANSWER x 2 + 2x – 24 ANSWER 2y 2 + 13y + 15.](https://reader035.fdocuments.in/reader035/viewer/2022062423/56649e6b5503460f94b68b5d/html5/thumbnails/11.jpg)
Warm-Up ExercisesEXAMPLE 4 Solve a polynomial equation
8. Solve the equation s2 – 2s = 24.
ANSWER The solutions of the equation are – 4 and 6.
GUIDED PRACTICE for Example 4
![Page 12: Warm-Up Exercises Find the product. 1.(x + 6)(x – 4) 2.(2y + 3)( y + 5) ANSWER x 2 + 2x – 24 ANSWER 2y 2 + 13y + 15.](https://reader035.fdocuments.in/reader035/viewer/2022062423/56649e6b5503460f94b68b5d/html5/thumbnails/12.jpg)
Warm-Up ExercisesEXAMPLE 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.
STEP 1Draw a diagram of two banners together.
SOLUTION
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Warm-Up ExercisesEXAMPLE 5 Solve a polynomial equation
STEP 2Write 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 rectangleA = l w
Substitute 33 for A and (4 + w + 4) for l.
Simplify and subtract 33 from each side.0 = w2 + 8w – 33
Factor right side.0 = (w + 11)(w – 3)
Zero-product propertyw + 11 = 0 or w – 3 = 0
33 = (4 + w + 4) w
Solve for w.w = – 11
ANSWERThe banner cannot have a negative width, so the width is 3 feet.
w = 3or
![Page 14: Warm-Up Exercises Find the product. 1.(x + 6)(x – 4) 2.(2y + 3)( y + 5) ANSWER x 2 + 2x – 24 ANSWER 2y 2 + 13y + 15.](https://reader035.fdocuments.in/reader035/viewer/2022062423/56649e6b5503460f94b68b5d/html5/thumbnails/14.jpg)
Warm-Up ExercisesGUIDED PRACTICE for Example 5
WHAT IF? In example 5, suppose the area of a banner is to be 10 square feet. What is the width of one banner?
9.
ANSWER 2 feet
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Warm-Up ExercisesDaily Homework Quiz
Factor the trinomial.
1. x2 – 6x – 16
2. y2 + 11y + 24
ANSWER (x +2)(x – 8)
3. x2 + x – 12
ANSWER (y +3)(y + 8)
ANSWER (x +4)(x – 3)
![Page 16: Warm-Up Exercises Find the product. 1.(x + 6)(x – 4) 2.(2y + 3)( y + 5) ANSWER x 2 + 2x – 24 ANSWER 2y 2 + 13y + 15.](https://reader035.fdocuments.in/reader035/viewer/2022062423/56649e6b5503460f94b68b5d/html5/thumbnails/16.jpg)
Warm-Up ExercisesDaily Homework Quiz
4. Solve a2 – a = 20
ANSWER – 4, 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?
5.
ANSWER 2 in. by 19 in.