determine the resulting polynomial:
$f(x) = 6x - 7$
$g(x) = 3x^2 + 5x + 4$
find: $f(x) \cdot g(x)$
answer
attempt 1 out of 2

Question

Accepted Answer

# Explanation:
## Step1: Apply Distributive Property
Multiply each term in $ f(x) = 6x - 7 $ by each term in $ g(x) = 3x^2 + 5x + 4 $.
$$
\begin{align*}
(6x - 7)(3x^2 + 5x + 4)&= 6x\cdot3x^2 + 6x\cdot5x + 6x\cdot4 - 7\cdot3x^2 - 7\cdot5x - 7\cdot4\
\end{align*}
$$
## Step2: Simplify Each Term
Calculate the product of each pair of terms:
$$
\begin{align*}
6x\cdot3x^2 &= 18x^3\
6x\cdot5x &= 30x^2\
6x\cdot4 &= 24x\
-7\cdot3x^2 &= -21x^2\
-7\cdot5x &= -35x\
-7\cdot4 &= -28\
\end{align*}
$$
## Step3: Combine Like Terms
Combine the $ x^2 $ terms and the $ x $ terms:
$$
\begin{align*}
18x^3 + (30x^2 - 21x^2) + (24x - 35x) - 28&= 18x^3 + 9x^2 - 11x - 28\
\end{align*}
$$
# Answer:
$ 18x^3 + 9x^2 - 11x - 28 $

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QUESTION IMAGE

Question

Explanation:

Step1: Apply Distributive Property

Step2: Simplify Each Term

Step3: Combine Like Terms

Answer: