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Five-Minute Check (over Lesson 9–1) Then/Now New Vocabulary Example 1: Identify Prime and Composite Numbers Example 2: Standardized Test Example Example 3: Factor Monomials Lesson Menu

Write (–5)(–5)(–5) using exponents. A. 52 B. (–5)2 C. 53 D. (–5)3 5-Minute Check 1

Write m ● m ● m ● m ● m ● m using exponents. A. m6 B. 2m3 C. 3m2 D. 6m 5-Minute Check 2

Write 4 ● a ● a ● (b + 1)(b + 1) using exponents. B. 4a2(b + 1)2 C. 4a(b + 1)2 D. 2a(b + 1)2 5-Minute Check 3

Evaluate the expression a0 + 13 if a = –3. B. 12 C. 13 D. 14 5-Minute Check 4

Evaluate the expression a2b3 if a = –3 and b = –1. C. –9 D. –10 5-Minute Check 5

Florence planted a sunflower and recorded its height each week Florence planted a sunflower and recorded its height each week. She noticed that its height doubled each week. Which expression represents the height of the sunflower after 10 weeks? A. 29 B. 210 C. 211 D. 212 5-Minute Check 6

You simplified expressions by multiplying. (Lesson 2–4) Write the prime factorizations of composite numbers. Factor monomials. Then/Now

prime number composite number prime factorization factor tree monomial Vocabulary

A. Determine whether 31 is prime or composite. Identify Prime and Composite Numbers A. Determine whether 31 is prime or composite. Find factors of 31 by listing the whole number pairs whose product is 31. 31 = 1 × 31 The number 31 has only two factors. Answer: Therefore, 31 is a prime number. Example 1 A

B. Determine whether 36 is prime or composite. Identify Prime and Composite Numbers B. Determine whether 36 is prime or composite. Find factors of 36 by listing the whole number pairs whose product is 36. 36 = 1 × 36 36 = 2 × 18 36 = 3 × 12 36 = 4 × 9 36 = 6 × 6 The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. Answer: Since the number has more than two factors, it is composite. Example 1 B

A. Determine whether 49 is prime or composite. A. prime B. composite C. neither D. prime and composite Example 1 CYP A

B. Determine whether 29 is prime or composite. A. prime B. composite C. neither D. prime and composite Example 1 CYP B

What is the prime factorization of 56? A 4 ● 14 B 22 ● 72 C 22 ● 7 D 23 ● 7 Read the Test Item You are asked to find the factors of 56 that are prime numbers. Construct a factor tree to find all of the prime numbers. Example 2

Write the prime factorization of 56. Solve the Test Item Write the prime factorization of 56. 56 8 ● 7 56 = 8 ● 7 4 ● 2 ● 7 8 = 4 ● 2 2 ● 2 ● 2 ● 7 4 = 2 ● 2 The prime factorization is 56 is 2 ● 2 ● 2 ● 7 or 23 ● 7. Answer: The answer is D. Example 2

What is the prime factorization of 72? B. 22 ● 33 C. 23 ● 32 D. 32 ● 7 Example 2 CYP

A. Factor the monomial 16p2q4. Factor Monomials A. Factor the monomial 16p2q4. 16p2q4 = 2 ● 2 ● 2 ● 2 ● p2 ● q4 16 = 2 ● 2 ● 2 ● 2 16p2q4 = 2 ● 2 ● 2 ● 2 ● p ● p ● q ● q ● q ● q p2 ● q4 = p ● p ● q ● q ● q ● q Answer: 16p2q4 = 2 ● 2 ● 2 ● 2 ● p ● p ● q ● q ● q ● q Example 3 A

B. Factor the monomial –21x2y. Factor Monomials B. Factor the monomial –21x2y. –21x2y = –1 ● 3 ● 7 ● x2 ● y –21 = –1 ● 3 ● 7 = –1 ● 3 ● 7 ● x ● x ● y x2 ● y = x ● x ● y Answer: –21x2y = –1 ● 3 ● 7 ● x ● x ● y Example 3 B

A. Factor the monomial 12a3b. A. 3 ● 4 ● a ● a ● a ● b B. 12 ● a ● a ● a ● b C. 2 ● 2 ● 3 ● a3 ● b D. 2 ● 2 ● 3 ● a ● a ● a ● b Example 3 CYP A

B. Factor –12w3z. A. –1 ● 2 ● 6 ● w ● w ● z B. –1 ● 2 ● 2 ● 3 ● w ● w ● z C. –1 ● 4 ● 3 ● w ● w ● w ● z ● z D. –1 ● 2 ● 2 ● 3 ● w ● w ● w ● z Example 3 CYP B

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