factoring by grouping algebra 1 lesson 9-8 (for help, go to lessons 9-2 and 9-3.) find the gcf of...

Factoring by GroupingALGEBRA 1 LESSON 9-8ALGEBRA 1 LESSON 9-8

(For help, go to Lessons 9-2 and 9-3.)

Find the GCF of the terms of each polynomial.

1. 6y2 + 12y – 4 2. 9r3 + 15r2 + 21r

3. 30h3 – 25h2 – 40h 4. 16m3 – 12m2 – 36m

Find each product.

5. (v + 3)(v2 + 5) 6. (2q2 – 4)(q – 5)

7. (2t – 5)(3t + 4) 8. (4x – 1)(x2 + 2x + 3)

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1. 6y2 + 12y – 4 2. 9r3 + 15r2 + 21r6y2 = 2 • 3 • y • y; 9r3 = 3 • 3 • r • r • r; 12y = 2 • 2 • 3 • y; 4 = 2 • 2; 15r2 = 3 • 5 • r • r; 21r = 3 • 7 • r;GCF = 2 GCF = 3r

3. 30h3 – 25h2 – 40h 4. 16m3 – 12m2 – 36m30h3 = 2 • 3 • 5 • h • h • h; 16m3 = 2 • 2 • 2 • 2 • m • m • m;25h2 = 5 • 5 • h • h; 12m2 = 2 • 2 • 3 • m • m;40h = 2 • 2 • 2 • 5 • h; 36m = 2 • 2 • 3 • 3 • m;GCF = 5h GCF = 2 • 2 • m = 4m

5. (v + 3)(v2 + 5) = (v)(v2) + (v)(5) + (3)(v2) + (3)(5)= v3 + 5v + 3v2 + 15= v3 + 3v2 + 5v + 15

Solutions

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Solutions (continued)

7. (2t – 5)(3t + 4)= (2t)(3t) + (2t)(4) + (–5)(3t) + (–5)(4)= 6t2 + 8t – 15t – 20= 6t2 – 7t – 20

6. (2q2 – 4)(q – 5)= (2q2)(q) + (2q2)(–5) + (–4)(q) + (–4)(–5)= 2q3 – 10q2 – 4q + 20

8. (4x – 1)(x2 + 2x + 3) = (4x)(x2) + (4x)(2x) + (4x)(3)+ (–1)(x2) + (–1)(2x) + (–1)(3)

= 4x3 + 8x2 + 12x – x2 – 2x – 3= 4x3 + (8 – 1)x2 + (12 – 2)x – 3= 4x3 + 7x2 + 10x – 3

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Factor 6x3 + 3x2 – 4x – 2.

6x3 + 3x2 – 4x – 2 = 3x2(2x + 1) – 2(2x + 1) Factor the GCF from each group of two terms.

= (2x + 1)(3x2 – 2) Factor out (2x + 1).

= 6x3 – 4x + 3x2 – 2 Use FOIL.

Check: 6x3 + 3x2 – 4x – 2 (2x + 1)(3x2 – 2)

= 6x3 + 3x2 – 4x – 2 Write in standard form.

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Factor 8t4 + 12t3 + 16t + 24.

8t4 + 12t3 + 16t + 24 = 4(2t4 + 3t3 + 4t + 6) Factor out the GCF, 4.

= 4[t3(2t + 3) + 2(2t + 3)] Factor by grouping.

= 4(2t + 3)(t3 + 2) Factor again.

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Factoring by GroupingFactor 24h2 + 10h – 6.

ALGEBRA 1 LESSON 9-8ALGEBRA 1 LESSON 9-8

Step 1: 24h2 + 10h – 6 = 2(12h2 + 5h – 3) Factor out the GCF, 2.

Step 2: 12 • –3 = –36 Find the product ac.

Step 4: 12h2 – 4h + 9h – 3 Rewrite the trinomial.

Step 5: 4h(3h – 1) + 3(3h – 1) Factor by grouping.

(4h + 3)(3h – 1) Factor again.

24h2 + 10h – 6 = 2(4h + 3)(3h – 1) Include the GCF in your final answer.

Step 3: Factors Sum–2(18) = –36 –2 + 18 = 16–3(12) = –36 –3 + 12 = 9 –4(9) = –36 –4 + 9 = 5

Find two factors of ac that have a sum b. Use mental math to determine a good place to start.

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A rectangular prism has a volume of 36x3 + 51x2 + 18x.

Factor to find the possible expressions for the length, width, and

height of the prism.

Factor 36x3 + 51x2 + 18x.

Step 1: 3x(12x2 + 17x + 6) Factor out the GCF, 3x.

Step 2: 12 • 6 = 72 Find the product ac.

Step 3: Factors Sum 4 • 18 4 + 18 = 22 6 • 12 6 + 12 = 18 8 • 9 8 + 9 = 17

Find two factors of ac that have sum b. Use mental math to determine a good place to start.

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(continued)

Step 4: 3x(12x2 + 8x + 9x + 6) Rewrite the trinomial.

Step 5: 3x[4x(3x + 2) + 3(3x + 2)] Factor by grouping.

3x(4x + 3)(3x + 2) Factor again.

The possible dimensions of the prism are 3x, (4x + 3), and (3x + 2).

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Factor each expression.

1. 10p3 – 25p2 + 4p – 10

2. 36x4 – 48x3 + 9x2 – 12x

3. 16a3 – 24a2 + 12a – 18

(5p2 + 2)(2p – 5)

3x(4x2 + 1)(3x – 4)

2(4a2 + 3)(2a – 3)

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factoring by grouping algebra 1 lesson 9-8 (for help, go to lessons 9-2 and 9-3.) find the gcf of...

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