Question

if ( x - 9 ) is a factor of ( x^2 - 5x - 36 ), what is the other factor?
( \bigcirc x - 4 )
( \bigcirc x + 4 )
( \bigcirc x - 6 )
( \bigcirc x + 6 )

Explanation:

Step1: Recall factoring quadratic

To factor \(x^2 - 5x - 36\) with one factor \(x - 9\), we need two numbers that multiply to \(-36\) and add to \(-5\). Let the other factor be \(x + a\), so \((x - 9)(x + a)=x^2+(a - 9)x-9a\).

Step2: Compare coefficients

Compare with \(x^2 - 5x - 36\). For the constant term: \(-9a=-36\), so \(a = 4\). For the linear term: \(a - 9=-5\), substituting \(a = 4\) gives \(4 - 9=-5\), which matches. So the other factor is \(x + 4\).

Answer:

B. \(x + 4\)