Suppose the roots of a polynomial are 3 / 4, - 7 / 8, - 3 / 8, and - 1 / 9. Which choice is a factor of the polynomial?

Given roots of the polynomial are 3/4, - 7/8, - 3/8 and - 1/9

that means graph crosses the x-axis at those x-values

hence we can write:

x=3/4, x=-7/8, x=-3/8 and x=-1/9

To cancel out denominator move denominator to the left side so we get:

4x=3, 8x=-7, 8x=-3 and 9x=-1

move every term on left side

4x-3=0, 8x+7=0, 8x+3=0 and 9x+1=0

(4x-3) (8x+7) (8x+3) (9x+1) = 0 (using zero product property)

Hence required factor of the polynomial will be (4x-3) (8x+7) (8x+3) (9x+1).

Hence any choice that matches with (4x-3) (8x+7) (8x+3) (9x+1) will be the answer.