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.
