david found and factored out the gcf of the polynomial 80b^4 - 32b^2c^3 + 48b^4c. his work is below. 1. gfc…

david found and factored out the gcf of the polynomial 80b^4 - 32b^2c^3 + 48b^4c. his work is below. 1. gfc of 80, 32, and 48: 16 2. gcf of b^4, b^2, and b^4: b^2 3. gcf of c^3 and c: c 4. gcf of the polynomial: 16b^2c 5. rewrite as a product of the gcf: 16b^2c(5b^2) - 16b^2c(2c^2) + 16b^2c(3b^2) 6. factor out gcf: 16b^2c(5b^2 - 2c^2 + 3b^2) which statements are true about davids work? check all that apply. the gcf of the coefficients is correct. the gcf of the variable b should be b^4 instead of b^2. 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.

david found and factored out the gcf of the polynomial 80b^4 - 32b^2c^3 + 48b^4c. his work is below. 1. gfc of 80, 32, and 48: 16 2. gcf of b^4, b^2, and b^4: b^2 3. gcf of c^3 and c: c 4. gcf of the polynomial: 16b^2c 5. rewrite as a product of the gcf: 16b^2c(5b^2) - 16b^2c(2c^2) + 16b^2c(3b^2) 6. factor out gcf: 16b^2c(5b^2 - 2c^2 + 3b^2) which statements are true about davids work? check all that apply. the gcf of the coefficients is correct. the gcf of the variable b should be b^4 instead of b^2. 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.

Answer

Explanation:

Step1: Analyze GCF of coefficients

The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80. The factors of 32 are 1, 2, 4, 8, 16, 32. The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. The GCF of 80, 32 and 48 is 16, so the GCF of the coefficients is correct.

Step2: Analyze GCF of variable b

For $b^{4},b^{2},b^{4}$, the lowest - power of b is $b^{2}$, so the GCF of b - terms is $b^{2}$, not $b^{4}$.

Step3: Analyze variable c

The terms $80b^{4}$ does not have the variable c, so c is not common to all terms and should not be factored out.

Step4: Analyze step 5

[ \begin{align*} 16b^{2}c(5b^{2})-16b^{2}c(2c^{2}) + 16b^{2}c(3b^{2})&=80b^{4}c-32b^{2}c^{3}+48b^{4}c\ &\neq80b^{4}-32b^{2}c^{3}+48b^{4}c \end{align*} ] The expression in step 5 is not equivalent to the given polynomial.

Step5: Analyze step 6

In step 6, $16b^{2}c(5b^{2}-2c^{2}+3b^{2})$ is obtained from $16b^{2}c(5b^{2})-16b^{2}c(2c^{2})+16b^{2}c(3b^{2})$ by applying the distributive property in reverse.

Answer:

The GCF of the coefficients is correct. The variable c is not common to all terms, so a power of c should not have been factored out. In step 6, David applied the distributive property.