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

2 answers:

4 0

the main formula is (cd)(x)=c(x).d(x) 
If c(x) = 4x – 2 and d(x) = x2 + 5x
so (cd)(x) = (4x – 2)(x2 + 5x)=4x^3+20x²-2x²-10x=4x^3+18x²-10x
so the answer is A: 4x^3+18x²-10x

dem82 [27]3 years ago

4 0

Answer:

Option 1st is correct.

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

Step-by-step explanation:

Given the functions:

$c(x) = 4x-2$

$d(x) = x^2+5x$

We have to find $(cd)(x)$ .

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

then;

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

Apply distributive property i. e $a \cdot (b+c) =a\cdot b+ a\cdot c$

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

Combine like terms ;

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

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What is the numerator of the simplified sum?

sashaice [31]

Answer:

4x + 6

Step-by-step explanation:

$\frac{x}{x² + 3x + 2} + \frac{3}{x + 1}$

To determine what the numerator would be, after simplifying both fractions, take the following steps:

Step 1: Factorise the denominator of the first fraction, x² + 3x + 2.

Thus,

x² + 2x + x + 2

(x² + 2x) + (x + 2)

x(x + 2) +1(x + 2)

(x + 1)(x + 2)

We would now have the following as our new fractions to add together and simplify:

$\frac{x}{(x + 1)(x + 2)} + \frac{3}{x + 1}$

Step 2: find the highest common factor of the denominator of both fractions.

Highest common factor of (x + 1)(x + 2) and (x + 1) = (x + 1)(x + 2)

Step 3: To add both fractions, divide the highest common factor gotten in step 2 by each denominator, and then multiply the result by the numerator of each fraction.

Thus,

$\frac{x}{(x + 1)(x + 2)} + \frac{3}{x + 1}$

$\frac{x + 3(x + 2)}{(x + 1)(x + 2)}$