Question

The binomial (y − 2) is a factor of y2 − 10y + 16. What is the other factor? (y − 5) (y + 5) (y − 8) (y + 8)

Answer 1

Answer: (y - 8)

Step-by-step explanation

Let the other factor be (y - c) for some constant c.

The idea is (y - 2)(y - c) expands to y^2 - 10y + 16

Use the FOIL rule or the box method to expand:

(y - 2)(y - c)

y^2 - cy - 2y + 2c

y^2 - (c+2)y + 2c

The last term 2c matches up with 16, so 2c = 16 leads to c = 8.

Therefore (y - c) updates to (y - 8)

I'll let the student confirm that (y - 2)(y - 8) = y^2 - 10y + 16.