Question

expand the expression to a polynomial in standard form: \\((-3x - 4)(x^2 + 3x - 5)\\)

Explanation:

Step1: Apply distributive property (FOIL for polynomials)

Multiply \(-3x\) by each term in \((x^2 + 3x - 5)\) and \(-4\) by each term in \((x^2 + 3x - 5)\):
\[

$$\begin{align*} -3x(x^2 + 3x - 5) - 4(x^2 + 3x - 5)&= -3x\cdot x^2 - 3x\cdot 3x + (-3x)\cdot (-5) - 4\cdot x^2 - 4\cdot 3x + (-4)\cdot (-5)\\ \end{align*}$$

\]

Step2: Simplify each term

Simplify the products:
\[

$$\begin{align*} &-3x^3 - 9x^2 + 15x - 4x^2 - 12x + 20\\ \end{align*}$$

\]

Step3: Combine like terms

Combine the \(x^2\) terms and the \(x\) terms:
\[

$$\begin{align*} &-3x^3 + (-9x^2 - 4x^2) + (15x - 12x) + 20\\ &= -3x^3 - 13x^2 + 3x + 20 \end{align*}$$

\]

Answer:

\(-3x^3 - 13x^2 + 3x + 20\)