Download Multiplying and Factoring

Multiplying
and Factoring
8-2
Vocabulary
Review
1. Place a ✓ if the number is a multiple of 10 and an ✗ if the number is NOT a
multiple of 10.
250
2
50
30
Vocabulary Builder
The factors of 2x2y
include
2, x, and y.
factor (noun) fak tur
Related Words: divide, factorable, factored form
Definition: A factor is a whole number or variable that divides another whole
number with a remainder of 0.
2. Cross out the expression that does NOT have x3 as a factor.
x5 HSM11_A1MC_0802_T13367
x2xy
12x2 (3x2)2
3. Circle the factor tree that shows a prime factorization.
6x2
6
6x2
x2
6x
x
6x2
2x
6x2
2
3x
3
x
x
HSM11_A1MC_0802_T13368
HSM11_A1MC_0802_T13370
HSM11_A1MC_0802_T13372 HSM11_A1MC_0802_T13373
Problem 1 Multiplying a Monomial and a Trinomial
Got It? What is a simpler form of 5n(3n3 2 n2 1 8)?
5.The simplified form of 5n(3n3 2 n2 1 8)
4. Distribute the 5n. Use the arrows to help you.
is
5n (3n3 –
=
Chapter 8
–
n2 +
8)
+
HSM11_A1MC_0802_T13374
230 2
1
.
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
Use Your Vocabulary
Finding the GCF of a pair of monomials is similar to finding the GCF of a pair of integers.
6. Circle the pair of numbers with a GCF of 4.
4 and 5
4 and 6
8 and 12
8 and 16 8x and 12x
8x and 16x 7. Circle the pair of monomials with a GCF of 4x.
4x and 5x
4x and 6x
8. Cross out the pair(s) of numbers whose GCF is NOT 6.
15 and 16
16 and 18
24 and 36
30 and 36 9. Cross out the pair(s) of monomials whose GCF is NOT 6y 2 .
15y2 and 16y2 16y2 and 18y2 24y2 and 36y2 30y2 and 36y2 Problem 2 Finding the Greatest Common Factor
Got It? What is the GCF of the terms of 3x4 2 9x 2 2 12x?
10. Circle the GCF of the numbers 3, 9, and 12.
1
2
3
6
9
12 11. Circle the GCF of x, x 2 , and x4 .
x0 x2 x
x3 x4
12. The GCF of the terms of 3x4 2 9x2 2 12x is .
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
Problem 3 Factoring Out a Monomial
Got It? What is the factored form of 9x6 1 15x4 1 12x 2 ?
3. Complete each factor tree.
1
9x 6
15x 4
3x
3
12x2
3x
x
3
3
x4
x
2x
x
5
x3
x
3x
2
5x
x
x
3
x2
HSM11_A1MC_0802_T13381
HSM11_A1MC_0802_T13377
14. Use the factor trees in Exercise 13 to write each prime factorization.
9x6 5 15x4 5 12x 2 5 HSM11_A1MC_0802_T13376
231
Lesson 8-2
15. 9x6, 15x4, and 12x2 have
common factors of 2
common factors of 3
common factors of 5
common factors of x
6. Multiply all common factors of 9x6 , 15x4 , and 12x2 to find the GCF.
1
17. Circle the next step to write 9x 6 1 15x4 1 12x 2 in factored form.
Add like terms.
Divide by 3x 6 . Factor the GCF from each term.
18. The factored form of 9x6 1 15x4 1 12x2 is
(
).
Problem 4 Factoring a Polynomial Model
Got It? A helicopter landing pad, or helipad, is sometimes marked
with a circle inside a square so that it is visible from the air. What is
the area of the region outside the circle but inside the square of the
helipad at the right? Write your answer in factored form.
19. Write an algebraic expression for the area of the square.
=(
Area of
)
6x
HSM11_A1MC_0802_T13384
)
Area of
= p(
1. Complete the problem-solving model below.
2
HSM11_A1MC_0802_T13385
Diagram
minus
area of
the region outside the
circle but inside the square
Relate
area of
area of
minus
the square
the circle
Write
(
)
2
p(
)
HSM11_A1MC_0802_T13386
Chapter 8
3x
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
20. Write an algebraic expression for the area of the circle.
232 22. Use the justifications below to find the area of the shaded region.
Area 5 ( )
2 p ( )
5 2 p 5 ( 2 p) x 2 5 x 2 ( Write the original equation.
Simplify each power.
Factor out x 2 .
2 ) Factor out the GCF of 36 and 9p.
23. The factored form of the area of the shaded region is .
Lesson Check • Do you UNDERSTAND?
Find the GCF of each pair of monomials.
14n2, 35n4 21n3, 18n2 7n2, 9
24. Factor each pair of monomials.
14n2 5 2 ? ? 2 and
35n4 5 ? ? 4
21n3 5 3 ? ? 3 and
18n2 5 ? ? and
9 5 7n2 5 ? 2 ? 2
? Draw a line from each pair of monomials in Column A to the GCF of the monomials
in Column B.
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
Column A
Column B
25. 14n2, 35n4 1
26. 21n3, 18n2 7n2
27. 7n2, 9
3n2
Math Success
Check off the vocabulary words that you understand.
factor
greatest common factor
standard form
factored form
Rate how well you can multiply a monomial by a polynomial.
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review
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Now I
get it!
10
233
Lesson 8-2