Answer :
To multiply
[tex]$$(-4x-1)\left(-7x^2+5x-2\right),$$[/tex]
we distribute each term from the first factor across every term in the second factor:
1. Multiply [tex]$-4x$[/tex] by each term in the second polynomial:
[tex]\[
\begin{aligned}
(-4x)\cdot(-7x^2) &= 28x^3, \\
(-4x)\cdot(5x) &= -20x^2, \\
(-4x)\cdot(-2) &= 8x.
\end{aligned}
\][/tex]
2. Multiply [tex]$-1$[/tex] by each term in the second polynomial:
[tex]\[
\begin{aligned}
(-1)\cdot(-7x^2) &= 7x^2, \\
(-1)\cdot(5x) &= -5x, \\
(-1)\cdot(-2) &= 2.
\end{aligned}
\][/tex]
3. Now, combine like terms:
- The [tex]$x^3$[/tex] term is:
[tex]\[
28x^3.
\][/tex]
- The [tex]$x^2$[/tex] terms are:
[tex]\[
-20x^2 + 7x^2 = -13x^2.
\][/tex]
- The [tex]$x$[/tex] terms are:
[tex]\[
8x - 5x = 3x.
\][/tex]
- The constant term is:
[tex]\[
2.
\][/tex]
Thus, the final product is:
[tex]$$
28x^3 - 13x^2 + 3x + 2.
$$[/tex]
This matches the first option.
[tex]$$(-4x-1)\left(-7x^2+5x-2\right),$$[/tex]
we distribute each term from the first factor across every term in the second factor:
1. Multiply [tex]$-4x$[/tex] by each term in the second polynomial:
[tex]\[
\begin{aligned}
(-4x)\cdot(-7x^2) &= 28x^3, \\
(-4x)\cdot(5x) &= -20x^2, \\
(-4x)\cdot(-2) &= 8x.
\end{aligned}
\][/tex]
2. Multiply [tex]$-1$[/tex] by each term in the second polynomial:
[tex]\[
\begin{aligned}
(-1)\cdot(-7x^2) &= 7x^2, \\
(-1)\cdot(5x) &= -5x, \\
(-1)\cdot(-2) &= 2.
\end{aligned}
\][/tex]
3. Now, combine like terms:
- The [tex]$x^3$[/tex] term is:
[tex]\[
28x^3.
\][/tex]
- The [tex]$x^2$[/tex] terms are:
[tex]\[
-20x^2 + 7x^2 = -13x^2.
\][/tex]
- The [tex]$x$[/tex] terms are:
[tex]\[
8x - 5x = 3x.
\][/tex]
- The constant term is:
[tex]\[
2.
\][/tex]
Thus, the final product is:
[tex]$$
28x^3 - 13x^2 + 3x + 2.
$$[/tex]
This matches the first option.
