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zhuklara
1 month ago
15

If c(x) = 4x – 2 and d(x) = x2 5x, what is (cd)(x)? 4x3 18x2 – 10x x2 9x – 2 16x2 4x – 6 4x2 20x – 2

Mathematics
2 answers:
Leona [12.6K]1 month ago
4 0
<span>
The fundamental formula is </span>(cd)(x) = c(x) × d(x) <span>
Given c(x) = 4x – 2 and d(x) = x² + 5x,
then </span>(cd)(x) = (4x – 2)(x² + 5x) = 4x³ + 20x² - 2x² - 10x = 4x³ + 18x² - 10x
<span>Hence, the solution is A: 4x³ + 18x² - 10x</span><span>

</span>
lawyer [12.5K]1 month ago
4 0

Answer:

The correct choice is the first option.

(cd)(x) = 4x^3+18x^2-10x

Detailed solution:

We are given the following functions:

c(x) = 4x-2

d(x) = x^2+5x

Our goal is to determine (cd)(x).

(cd)(x) = c(x)d(x)

Next,

(cd)(x) = (4x-2)(x^2+5x) = 4x(x^2+5x)-2(x^2+5x)

Use the distributive property, which means a \cdot (b+c) =a\cdot b+ a\cdot c

(cd)(x) = 4x^3+20x^2-2x^2-10x

Group like terms together;

(cd)(x) = 4x^3+18x^2-10x

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