type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar…

type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar. the factors of 5y² - 2y - 7 are (5y - 7) and ( ).

type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar. the factors of 5y² - 2y - 7 are (5y - 7) and ( ).

Answer

Explanation:

Step1: Use FOIL method concept

We know that if ((ay + b)(cy + d)=acy^{2}+(ad + bc)y+bd). Here (acy^{2}+(ad + bc)y+bd = 5y^{2}-2y - 7), (ac = 5), (bd=-7) and (ad+bc=-2). Given one factor is (5y - 7), let the other factor be (my + n). Then ((5y - 7)(my + n)=5my^{2}+(5n-7m)y-7n). Comparing coefficients: (5m = 5), so (m = 1).

Step2: Solve for the remaining part

Since (5n-7m=-2) and (m = 1), we substitute (m) into the equation: (5n-7\times1=-2), which simplifies to (5n=5), so (n = 1).

Answer:

(y + 1)