Download Reteach Factoring by GCF

Name
Date
Class.
(-L
Reteach
Factoring by GCF
The Distributive Property states:
a(b + c) = ab + ac
Factoring by GCF reverses the Distributive Property:
ab + ac = a(b + c)
Factor 12x3 + 21 x2 + 15x. Check your answer.
Step 1: Find the GCF oi all the terms in the polynomial.
The factors of 12x3 are: 1, 2, 3, 4, 6, 12, x, x, x '
The factors of 21 x2 are: 1, 3, 7, 21, x, x
The GCF is 3x.
The factors of 15xare: 1, 3, 5, 15, x
Step 2: Write terms as products using the GCF.
12x 3 + 21x 2 +
15x
(3x)4x2 + (3x)7x + (3x)5
Step 3: Use the Distributive Property to factor out the GCF.
3x(4x2 + 7x+ 5)
Check:
3x(4x2 + 7x + 5) = 12x3 + 21x2 + 15x /
Factor 5(x - 3) + 4x(x - 3).
Step 1: Find the GCF of all the terms
polynomial.
s i i u o iin
i i the
nit? [jwiyiiv-'i
The factors of 5 (x - 3) are5:5, ( x - 3 )
1
re: 4, x, (x- 3)J
The factors of 4x(x - 3) are
The GCF is (x-3).
The terms are already written as products with the GCF.
Step 2: Use the Distributive Property to factor out the GCF.
(x-3)(5 + 4x)
Factor each polynomial.
1. 20x2 - 15x
2. 44a2
3. 24y - 36x
5. 3a(a + 4) - 2(a + 4)
6. 4y(4y + 1) + (4y + 1)
Factor each expression.
4. 5x(x+ 7) + 2(x+ 7)
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14
Holt Algebra 1
Name
Date
Class.
Practice B
Factoring by GCF
Factor each polynomial. Check your answer.
1. 8c2 + 7c
2. 3/73 + 12n2
4. -8s4 + 20f3 - 28
5.
3. 15x5- 18x
18n-24n
6. -5m4 - 5m + 5m'
7. A ball is hit vertically into the air using a paddle at a
speed of 32 ft/sec. The expression -16?2 + 327 gives
the ball's height after t seconds. Factor this expression.
8. The area of Margo's laptop computer screen is
12x2 -f 3xin2. Factor this polynomial to find expressions
for the dimensions of her computer screen.
Factor each expression.
9. 3m(m + 5) + 4(m + 5)
10. 166Gb -3) + O b - 3 )
Factor each polynomial by grouping.
11. 2x3 + 8x2 + 3x + 12
12.
13. 10of2 - 6d+ 35d ~ 21
14. 12n3-
15. 5b4 - 1563 + 3 - b
16. /3 - 5r + 1 0 - 2 ?
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
12
3n
10
Holt Algebra 1
Name
Date
Practice C
Class.
1-1°
Factoring by GCF
Factor each polynomial. Check your answer.
I. 8x4 -
2. -12ab3 + 206
3. 16/rr - 2nJ + 30m
4. 27y 4 -- 72y3 + 9y
5. -5x5 + 35x4 - 30x3
6. 16x6y+ 16x2y4 + 32x3y2
7. The expression used for finding the surface area
of a cylinder is 2irr2 + 2^rh. Factor this expression.
8. The area of a hallway rug is j|x2 + ^xft 2 . Factor
this polynomial to find expressions for the dimensions
of the rug.
Factor each expression.
10. 9nr(m + 7) + 5 ( m + 7)
9. 10(/c- 2) + 7k(k- 2)
Factor each polynomial by grouping.
11. 2t3 + 6t2 + t + 3
12. 3n4 + 2n 3 - 15n- 10
13. 12a2 + 30a- 14a- 35
14. -28n2 - 14+ 10n5 + 5n3
15. 3d4 - 24b3 + 8 - b
16. 3x3 - 12x2 + 20 - 5x
Copyright © by Holt, Rinehart and Winston.
AH rights reserved.
13
Holt Algebra 1
LESSON 8-2
Practice A
2.)
1. x;5
2. 5; m3
3- 5; y5; 2
4. 2y*(5 + 6y)
5. 6f(-2f4 + 1)
6. 3x2(2x2 + 5x +1)
7. 5/H+8)
8. 3xand x + 8
9. (c/+2)(4Gf + 9)
10. (x-5)(12 + 7x)
11. 3n2; 12; 3; 3; (n + 3)(n2
12. (2x + 5)(x2+ 1)
13. 2/; 6; y; 2; y; y; y; 2; (y -2)(2y 2 -3)
14. (m - 3)(4m2 - 5)
Practice B T/ £r 2-
1. c(8c + 7)
2. 3n2(n + 4)
3. 3x(5x4 - 6)
4. 4(-2s4 + 5^-7)
5. 6n(n5 + 3n 3 -4)
6. 5m 2 (-m 2 -m+1)
7. 16fH+2)
8. 3x and 4x + 1
9. (m + 5)(3m + 4)
10. (t>-3)(166+1)
11. (x + 4)(2x2 + 3)
12. (4n + 3)(n 2 +1)
13. (5d-3)(2tf + 7)
14. (4n - 5)(3n2 - 2)
15. (b-3)(56 3 -1)
16. (?-2)(t-S)
Practice C Tiff 3
1. 4x 2 (2x 2 -3)
2. 4fa(-3ab2 + 5)
3. 2(8m2 - n3 + 15m)
4. 9/(3/-8/+1)
5. -5x 3 (x 2 -7x+6)
6. 16x2y(x4 + 3^ + 2xy
7. 2^r(r+ /i)
8. — x and 3x+ 1
9. (/f-2)(10 + 7/c)
11. (f + 3)(2<2 + 1)
10.
+ 7)(9m2 + 5
12.
n + 2)(n 3 -5)
13. (6a-7)(2a + 5)
14. (2n 2 + 1)(5n3-14)
16. (x-4)(3x 2 -5)
15. (3b3 - 1 )(fc - 8)
he original content are the responsibility of the instructor.
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Holt McDougal Algebra 1