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)

given polynomial 80b^4 – 32b^2c^3 + 48b^4c.

to find: factor put gcf.

solution: in order to factor a gcf of ploynomial, we always look over coefficent of each term and factor out gcf of those coefficents .

then we choose first variable terms in all terms and find gcf of first variable terms.

then choose another variable and factor out gcf of those terms.

david choose 80, 32 and 48 and factored out gcf of those numbers as 16.

so first step is taken by david is correct.

then he choose b variable factors   b^4,b^2, b^4 and found gcf b^2 which is correct.

then in third step he choose c^3, and c and found gcf c.

here devid mistaken. there are three terms and we need to take gcf of variable(s) that would be all terms.

variable c is not there in first term 80b^4.

therefore, final gcf would be just product of gcf found in first two steps.

that is 16 times b^2 = 16b^2.

therefore, following statements would be correct statements :

a)the gcf of the coefficients is correct.

b)the variable c is not common to all terms, so a power of c should not have been factored out.

c) in step 6, david applied the distributive property.

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation: