Question

product and quotient functions
m(x) = x² + 4x
(mn)(x) =
x² + 4x(x)
(x² + 4x)(x) ✔️
complete
which is equal to:
x³ + 4x² ✔️
5x²
4x⁴
complete
n(x) = x
evaluate (mn)(x) for x = -3.
(mn)(-3) =
done ✔️

Explanation:

Step1: Recall the formula for \((mn)(x)\)

We know that \((mn)(x)=m(x)\cdot n(x)\). From the problem, \(m(x)=x^{2}+4x\) and \(n(x) = x\), and we already found that \((mn)(x)=(x^{2}+4x)(x)=x^{3}+4x^{2}\).

Step2: Substitute \(x = - 3\) into \((mn)(x)\)

Now we substitute \(x=-3\) into the expression \(x^{3}+4x^{2}\).
First, calculate \(x^{3}\) when \(x = - 3\): \((-3)^{3}=-27\) (because \((-3)\times(-3)\times(-3)=9\times(-3)=-27\)).
Then, calculate \(4x^{2}\) when \(x=-3\): \(x^{2}=(-3)^{2}=9\), so \(4x^{2}=4\times9 = 36\).

Step3: Add the two results together

Now we add the results of \(x^{3}\) and \(4x^{2}\) when \(x = - 3\): \(-27+36 = 9\).

Answer:

\(9\)