Question

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

Explanation:

Step1: Recall factored quadratic form

Let the missing factor be $(ay + b)$. Then:
$$(5y - 7)(ay + b) = 5y^2 - 2y - 7$$

Step2: Match leading coefficient

For $y^2$ term: $5a = 5$, so $a=1$.

Step3: Match constant term

For constant term: $-7b = -7$, so $b=1$.

Step4: Verify middle term

Check $5y(1) + (-7)(1)y = 5y -7y = -2y$, which matches.

Answer:

$y + 1$