Factoring Polynomials: GCF Assignment

David found and factored out the GCF of the polynomial 80b4 - 32b2c3 + 48b4c. His work is below. GFC of 80, 32, and 48: 16 GCF of b4, b2, and b4: b2 GCF of c3 and c: c GCF of the polynomial: 16b2c Rewrite as a product of the GCF:16b2c(5b2) - 16b2c(2c2) + 16b2c(3b2) Factor out GCF: 16b2c(5b2 - 2c2 + 3b2) Which statements are true about David's work? Check all that apply. The GCF of the coefficients is correct. The GCF of the variable b should be b4 instead of b2. The variable c is not common to all terms, so a power of c should not have been factored out. The expression in step 5 is equivalent to the given polynomial. In step 6, David applied the distributive property.

1 3 5

Which of the following terms have a GCF of 6p3? Select two options.

1 4

Which statements are true about the polynomial 28vw + 49v + 35w? Check all that apply. The coefficients have no common factors other than 1. There are no common variables among all three terms. The GCF of the polynomial is 7v. Each term written as the product, where one factor is the GCF, is 7(28vw) + 7(49v) + 35(w). The resulting expression when factoring out the GCF is 7(4vw + 7v + 5w).

2 5

What is the factored form of the polynomial 27x2y - 43xy2? xy(27x - 43y) x2y2(27 - 43) 3xy(9x - 17y) 3x2y(9 - 14y)

A.) xy(27x - 43y)

4x2 is the GCF of this polynomial. 20x2y + 56x3 - ? Which could be the mystery term? 22x3 24x2y 26x2y 28y3

B.) 24x2y

What is the GCF of h4 and h8? h2 h4 h8 h12

B.) h4

Factor 26r3s + 52r5 - 39r2s4. What is the resulting expression? 13(2r3s + 4r5 - 3r2s4) 13r2s(2r + 4r3 - 3s3) 13r2(2rs + 4r3 - 3s4) 13r2(26r3s + 52r5 - 39r2s4)

C.) 13r2(2rs + 4r3 - 3s4)

Find the GCF of 44j5k4 and 121j2k6. Find the GCF of 44 and 121. Find the GCF of j5 and j2. Find the GCF of k4 and k6. What is the GCF of 44j5k4 and 121j2k6? 4j3k2 4j2k4 11j3k2 11j2k4

D.) 11j2k4

Joan is building a sandbox in the shape of a regular pentagon. The perimeter of the pentagon is 35y4 - 65x3 inches. What is the length of one side of the sandbox? 5y - 9 inches 5y4 - 9x3 inches 7y - 13 inches 7y4 - 13x3 inches

D.) 7y4 - 13x3 inches

Isiah determined that 5a2 is the GCF of the polynomial a3 - 25a2b5 - 35b4. Is he correct? Explain.

No, Isiah is not correct. The GCF of the coefficients is 1, and there are no common variables among all three terms of the polynomial. 5b4 is a factor of -25a2b5 and -35b4, but not a3. Additionally, a2 is a factor of a3 and -25a2b5, but not -35b4.