Question

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 1

(y+1)

Explanation:

Answer 2

(y +1)

Explanation:

When you multiply the binomials (ay+b)(cy+d), the product is ...

acy² +(ad +bc)y +bd

In this problem, you know the product and you know one of the factors (ay+b) = (5y -7), so ...

• ac = 5
• a = 5
• bd = -7
• b = -7

These tell you ...

c = ac/a = 5/5 = 1

d = bd/b = -7/7 = 1

Then the other factor is ...

(cy+d) = (y+1)

____

Check

We can check this by looking at the y-term:

(ad+bc) = -2 . . . . from the given polynomial

(5)(1) +(-7)(1) = 5-7 = -2 . . . . answer checks OK