Middle School

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If \( f(x) = x - 7 \) and \( g(x) = 2x + 5 \), then what is \( f(x) \cdot g(x) \)?

A. \( 2x^2 - 9x - 35 \)
B. \( 2x^2 + 9x - 35 \)
C. \( 2x^2 - 2x - 35 \)
D. \( 3x^2 - 9x - 35 \)
E. \( 3x - 2 \)

Answer :

Answer:

2x² - 9x - 35

Step-by-step explanation:

f(x) × g(x) = (x - 7)(2x + 5)

Each term in the second factor is multiplied by each term in the first factor, that is

x(2x + 5) - 7(2x + 5) ← distribute both parenthesis

= 2x² + 5x - 14x - 35 ← collect like terms

= 2x² - 9x - 35

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Rewritten by : Barada

The result of f(x) * g(x) is 2x^2 - 9x - 35.

If f(x) = x - 7 and g(x) = 2x + 5, then to find f(x) * g(x), we need to multiply the two functions together.

Here's the step-by-step multiplication process:

Multiply the first term of f(x) by each term of g(x): x * (2x + 5) = 2x2 + 5x.

Add the results from steps 1 and 2 to get the final result: 2x^2 + 5x - 14x - 35.

Combine like terms: 2x^2 + (5x - 14x) - 35 = 2x^2 - 9x - 35.

Therefore, the product f(x) * g(x) is 2x^2 - 9x - 35.