Home » Test Prep » PSAT Test » If f(x) = 3x – 2, g(x) = 2x + 3, and h(x) = f(x) × g(x), then h(x) = ?
If f(x) = 3x – 2, g(x) = 2x + 3, and h(x) = f(x) × g(x), then h(x) = ?
A. 6x2 + 5x – 6
B. 6x – 1
C. 6x2 – 4x – 6
D. 6x2 + 9x + 6
E. 6x – 6
Correct Answer: A
Explanation/Reference:
Explanation:
To find what h(x) equals, you must know how to multiply f(x) times g(x), or, you must know how to multiply binomials. The best way to multiply monomials is the FOIL (first, outside, inside, last) method, as shown below:
h(x) = f(x) × g(x) = (3x – 2) × (2x + 3) Multiply the First terms
3x × 2x = 6x2 Multiply the Outside terms:
3x × 3 = 9x Multiply the Inside terms:
-2 × 2x = -4x Note: this step yields a negative number because the product of the two terms is negative.
Multiply the Last terms:
-2 × 3 = -6 Note: this step yields a negative number too! Putting the results together, you get:
(3x – 2) × (2x + 3) = 6x2 + 9x – 4x – 6 Finally, combine like terms, and you get:
h(x) = 6x2 + 5x – 6
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