Question

which of the following is a factor of ( x^2 - 3x - 54 )?

a ( (x - 27) )

b ( (x + 2) )

c ( (x - 6) )

d ( (x - 9) )

e none of these

Explanation:

Step1: Factor the quadratic

To factor \(x^2 - 3x - 54\), we need two numbers that multiply to \(-54\) and add to \(-3\).
The numbers are \(-9\) and \(6\) because \((-9)\times6 = -54\) and \(-9 + 6 = -3\).
So, \(x^2 - 3x - 54=(x - 9)(x + 6)\).

Step2: Identify the factor

From the factored form, the factors are \((x - 9)\) and \((x + 6)\). Looking at the options, \((x - 9)\) (option D) is a factor.

Answer:

D. \((x - 9)\)