the binomial (y - 2) is a factor of y² - 10y + 16. what is the other factor?\n(y - 5)\n(y + 5)\n(y - 8)\n(y…

Explanation:

Step1: Use polynomial long - division

Divide $y^{2}-10y + 16$ by $y - 2$.

Step2: Set up long - division

$\frac{y^{2}-10y + 16}{y - 2}$. First, divide the leading term of the dividend $y^{2}$ by the leading term of the divisor $y$, we get $y$. Multiply $y-2$ by $y$ to get $y^{2}-2y$. Subtract this from the dividend: $(y^{2}-10y + 16)-(y^{2}-2y)=-8y + 16$.

Step3: Continue long - division

Divide the leading term of the new dividend $-8y$ by the leading term of the divisor $y$, we get $-8$. Multiply $y - 2$ by $-8$ to get $-8y+16$. Subtract this from the new dividend: $(-8y + 16)-(-8y + 16)=0$.

Answer:

C. $(y - 8)$