Question

If f(x) = 4x+9 and g(x) = x-6, what is f(x) times g(x)?

A.) x^2 - 15x + 8
B.) 4x^2 - 15x - 54
C.) x^2 - 54x - 15
D.) 4x^2 + 8x -54

Answer 1

B.) 4x^2 - 15x - 54

Explanation:

You want the product f(x)·g(x) when f(x) = 4x+9 and g(x) = x-6.

Binomial multiplication

The distributive property can be used to find the product. Each term of one binomial is multiplied by every term of the other, and like terms are combined.

f(x)·g(x) = (4x +9)·(x -6)

= 4x(x -6) +9(x -6)

= 4x² -24x +9x -54 = 4x² +(-24 +9)x -54

f(x)·g(x) = 4x² -15x -54 . . . . . . . . . . matches choice B

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Additional comment

The product of two binomials is sometimes described using the mnemonic FOIL, for First, Outer, Inner, Last. These refer to the locations of the terms involved in the four products

• (4x +9)·(x -6) — First
• (4x +9)·(x -6) — Outer
• (4x +9)·(x -6) — Inner
• (4x +9)·(x -6) — Last

These products are the same as the ones we show above.

The FOIL mnemonic is only helpful for two binomials. Any polynomials can be multiplied using the distributive property.