Which expression serves as a factor of x² + 3x - 54?

To determine which expression serves as a factor of (x^2 + 3x - 54), we can attempt to factor the quadratic expression. The process involves identifying two numbers that multiply to the constant term (-54) and add up to the coefficient of the linear term (3).

First, we look for pairs of factors of -54. The pairs include:

• 1 and -54

• 2 and -27

• 3 and -18

• 6 and -9

• -1 and 54

• -2 and 27

• -3 and 18

• -6 and 9

Among these, the pair that adds up to 3 is 9 and -6. This means we can rewrite the quadratic expression as:

[

x^2 + 9x - 6x - 54

]

Grouping the terms, we factor it:

[

x(x + 9) - 6(x + 9)

]

This can be factored further into:

[

(x - 6)(x + 9)

]

From this factoring, it's evident that (x + 9) is one of the factors of the original quadratic expression