Question

If c(x) = 4x – 2 and d(x) = x2 + 5x, what is (cxd)(x)

Answer 1

Answer:

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

Step-by-step explanation:

We have two functions:

c(x) = 4x – 2

d(x) = x2 + 5x

And we need to find (cxd)(x) which is the multiplication of both functions:

(cxd)(x) = (4x – 2)(x^2 + 5x) = 4x × x^2 + 20x^2 - 2x^2 -10x

= 4x^3 + 18x^2 - 10x

Then: (cxd)(x) = 4x^3 + 18x^2 - 10x

Answer 2

Answer: $(c*d)(x)=4x^3+18x^2-10x$

Step-by-step explanation:

You know that the function $c(x)$ and the function $d(x)$ are:

$c(x) = 4x - 2\\\\d(x) = x^2 + 5x$

Then, in order to find $(c*d)(x)$ you need to multiply the function $c(x)$ by the function $d(x)$:

$(c*d)(x)=(4x - 2)(x^2 + 5x)$  

You must remember the Product of powers property, which states that:

$(a^m)(a^n)=a^{(m+n)}$

Now you can apply Distributive property:

$(c*d)(x)=4x^3+20x^2-2x^2-10x$

Finally, add the like terms. Then:

$(c*d)(x)=4x^3+18x^2-10x$