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(c) We factor out the GCF of the three terms, which is x². 3x4 – 5x3 + x2 = x²(3x²) – x²([x) + x²(1) Write the last term, x?, as x²(1) = x2(Ox2 - 5x + 1) Factor out the GCF, x2. We check by multiplying: x2(3x O) = 3x4 - 5x3 + x². - 5x + 3 Factor: (a) 5f + 45 (b) 16s²t² – 40s³t and (c) y6 – 9y4 – y3 (a) (b) (c)

(c) We factor out the GCF of the three terms, which is x². 3x4 – 5x3 + x2 = x²(3x²) – x²([x) + x²(1) Write the last term, x?, as x²(1) = x2(Ox2 - 5x + 1) Factor out the GCF, x2. We check by multiplying: x2(3x O) = 3x4 - 5x3 + x². - 5x + 3 Factor: (a) 5f + 45 (b) 16s²t² – 40s³t and (c) y6 – 9y4 – y3 (a) (b) (c)

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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(c) We factor out the GCF of the three terms, which is x². 3x4 – 5x3 + x² = x²(3x²) – x²([ ]x) + x²(1) Write the last term, x², as x²(1) = x2(Ox2 - 5x + 1) Factor out the GCF, x². We check by multiplying: x2(3x² – 5x + |) = 3x4 – 5x3 + x². 3 Factor: (a) 5f + 45 (b) 16s²t² – 40s³t and (c) y6 – 9yª – y3 (a) (b) (c)
Transcribed Image Text:(c) We factor out the GCF of the three terms, which is x². 3x4 – 5x3 + x² = x²(3x²) – x²([ ]x) + x²(1) Write the last term, x², as x²(1) = x2(Ox2 - 5x + 1) Factor out the GCF, x². We check by multiplying: x2(3x² – 5x + |) = 3x4 – 5x3 + x². 3 Factor: (a) 5f + 45 (b) 16s²t² – 40s³t and (c) y6 – 9yª – y3 (a) (b) (c)
Factor: (a) 8m + 24, (b) 35a³b² - 14a?b³, and (c) 3x4 – 5x3 + x2 First, we will determine the GCF of the terms of the polynomial. Then we will write each term of the polynomial as the product of the GCF and one other factor. We can then use the distributive property to factor out the GCF. (a) Since the GCF of 8m and 24 is 8, we write 8m and 24 as the product of 8 and one other factor. 8m + 24 = 8•m+ 8•3 (m + 3) Factor out the GCF, 8. To check, we multiply: 8(m + 3) = 8 · m + 8 • 3 = 8m + 24. Since we obtain the original polynomial, 8m + 24, the factorization is correct. Remember to factor out the greatest common factor, not just a common factor. If we factored out 4 in the previous example, we would get 8m + 24 = 4(2m + 6) However, the terms in red within parentheses have a common factor of 2, indicating that the factoring is not complete. (b) First, find the GCF of 35a³b² and 14a²b³. 35a3b2 = :7•a•a•a•b•b The GCF is 7a²b² 14a?b3 =||:7•a•a•b •b•b %3D Now, we write 35a b2 and 14a?b3 as the product of the GCF, 7a2b?, and one other factor. 35a³b2 – 14a²b3 = 7a²b² • – 7a²b² • 2b а — = 7a?b?(5a -O b) 7a?b?. Factor out the GCF, We check by multiplying: 7a?b?(5a – 2b) = 35a³b² – a?b³. %D (c) We factor out the GCF of the three terms, which is x2.
Transcribed Image Text:Factor: (a) 8m + 24, (b) 35a³b² - 14a?b³, and (c) 3x4 – 5x3 + x2 First, we will determine the GCF of the terms of the polynomial. Then we will write each term of the polynomial as the product of the GCF and one other factor. We can then use the distributive property to factor out the GCF. (a) Since the GCF of 8m and 24 is 8, we write 8m and 24 as the product of 8 and one other factor. 8m + 24 = 8•m+ 8•3 (m + 3) Factor out the GCF, 8. To check, we multiply: 8(m + 3) = 8 · m + 8 • 3 = 8m + 24. Since we obtain the original polynomial, 8m + 24, the factorization is correct. Remember to factor out the greatest common factor, not just a common factor. If we factored out 4 in the previous example, we would get 8m + 24 = 4(2m + 6) However, the terms in red within parentheses have a common factor of 2, indicating that the factoring is not complete. (b) First, find the GCF of 35a³b² and 14a²b³. 35a3b2 = :7•a•a•a•b•b The GCF is 7a²b² 14a?b3 =||:7•a•a•b •b•b %3D Now, we write 35a b2 and 14a?b3 as the product of the GCF, 7a2b?, and one other factor. 35a³b2 – 14a²b3 = 7a²b² • – 7a²b² • 2b а — = 7a?b?(5a -O b) 7a?b?. Factor out the GCF, We check by multiplying: 7a?b?(5a – 2b) = 35a³b² – a?b³. %D (c) We factor out the GCF of the three terms, which is x2.
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