Question

the expression ( y^2 - 10y + 24 ) has a factor of ( y - 4 ). what is another factor of ( y^2 - 10y + 24 )?
( \bigcirc ) ( y - 20 )
( \bigcirc ) ( y - 14 )
( \bigcirc ) ( y - 8 )
( \bigcirc ) ( y - 6 )

Explanation:

Step1: Recall factoring quadratic

For \(y^2 - 10y + 24\), we know one factor is \(y - 4\). Let the other factor be \(y - a\). Then \((y - 4)(y - a)=y^2-(4 + a)y + 4a\).

Step2: Compare coefficients

Compare with \(y^2 - 10y + 24\). So \(-(4 + a)=-10\) (coefficient of \(y\)) and \(4a = 24\) (constant term). From \(4a = 24\), we get \(a = 6\). So the other factor is \(y - 6\).

Answer:

D. \(y - 6\)