simplify the following polynomial expression.
$$(5x^3 + 4x^2 + 6x - 3) + (-2x^3 + 3x^2 - 7x + 9) - (5x + 3)(4x^2 + x - 1)$$
- $-17x^3 - 10x^2 + x + 18$
- $-23x^3 - 24x^2 + 3x + 9$
- $-23x^3 - 24x^2 + 3x + 18$
- $-17x^3 - 10x^2 + x + 9$

Question

Accepted Answer

# Explanation:
## Step1: Expand the product term
First, expand $(5x + 3)(4x^2 + x - 1)$ using the distributive property (FOIL for polynomials):
$$
\begin{align*}
(5x)(4x^2)+(5x)(x)+(5x)(-1)+3(4x^2)+3(x)+3(-1)&=20x^3 + 5x^2 - 5x + 12x^2 + 3x - 3\
&=20x^3+(5x^2 + 12x^2)+(-5x + 3x)-3\
&=20x^3 + 17x^2 - 2x - 3
\end{align*}
$$
## Step2: Combine the first two polynomials
Now, add $(5x^3 + 4x^2 + 6x - 3)$ and $(-2x^3 + 3x^2 - 7x + 9)$:
$$
\begin{align*}
&(5x^3 + 4x^2 + 6x - 3)+(-2x^3 + 3x^2 - 7x + 9)\
=&(5x^3 - 2x^3)+(4x^2 + 3x^2)+(6x - 7x)+(-3 + 9)\
=&3x^3 + 7x^2 - x + 6
\end{align*}
$$
## Step3: Subtract the expanded product from the combined polynomial
Subtract $20x^3 + 17x^2 - 2x - 3$ from $3x^3 + 7x^2 - x + 6$:
$$
\begin{align*}
&(3x^3 + 7x^2 - x + 6)-(20x^3 + 17x^2 - 2x - 3)\
=&3x^3 + 7x^2 - x + 6 - 20x^3 - 17x^2 + 2x + 3\
=&(3x^3 - 20x^3)+(7x^2 - 17x^2)+(-x + 2x)+(6 + 3)\
=&-17x^3 - 10x^2 + x + 9
\end{align*}
$$
# Answer:
$-17x^3 - 10x^2 + x + 9$ (the fourth option: $-17x^3 - 10x^2 + x + 9$)

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QUESTION IMAGE

Question

Explanation:

Step1: Expand the product term

Step2: Combine the first two polynomials

Step3: Subtract the expanded product from the combined polynomial

Answer: