Question

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

Answer 1

y-8

y2-2y-8y+16

y(y-2)-8(y-2)

(y-8)(y-2)

***

Answer 2

Answer: The other factor is (y-8).

Step-by-step explanation: The given quadratic expression is $y^{2}-10y+16.$

One of the factors of the above quadratic expression is given to be $(y-2)$. To find the other factor, either we can divide $y^{2}-10y+16$ by $(y-2)$ or we can factorise the quadratic expression into two linear factors.

Here, we will follow the second approach and will try to factorise the expression as follows-

$y^{2}-10y+16\\ =y^{2}-8y-2y+16\\ =y(y-8)-2(y-8)\\=(y-2)(y-8).$

Thus, the other factor is (y-8).