the expression $y^{2}-10y + 24$ has a factor of $y - 4$. what is another factor of $y^{2}-10y + 24$?\n$y…

the expression $y^{2}-10y + 24$ has a factor of $y - 4$. what is another factor of $y^{2}-10y + 24$?\n$y - 20$\n$y - 14$\n$y - 8$\n$y - 6$

the expression $y^{2}-10y + 24$ has a factor of $y - 4$. what is another factor of $y^{2}-10y + 24$?\n$y - 20$\n$y - 14$\n$y - 8$\n$y - 6$

Answer

Explanation:

Step1: Use polynomial long - division

We divide $y^{2}-10y + 24$ by $y - 4$. Set up the long - division: $\frac{y^{2}-10y + 24}{y - 4}$. First, divide the leading term of the numerator $y^{2}$ by the leading term of the denominator $y$. We get $y$. Multiply $y-4$ by $y$: $y(y - 4)=y^{2}-4y$. Subtract this from the numerator: $(y^{2}-10y + 24)-(y^{2}-4y)=y^{2}-10y + 24 - y^{2}+4y=-6y + 24$.

Step2: Divide the new leading term

Divide the leading term of $-6y + 24$ (which is $-6y$) by the leading term of $y - 4$ (which is $y$). We get $-6$. Multiply $y - 4$ by $-6$: $-6(y - 4)=-6y+24$. Subtract: $(-6y + 24)-(-6y + 24)=0$. So, $y^{2}-10y + 24=(y - 4)(y - 6)$.

Answer:

D. $y - 6$