Question

Directions - Multiply the polynomials.



​
−
5
x
2
(
6
x
3
−
x
+
2
)
−5x
2
(6x
3
−x+2)

Answer 1

To multiply the polynomial \(-5x^2\) by each term inside the parentheses \((6x^3 - x + 2)\), you can distribute \(-5x^2\) to each term.

Here's the step-by-step multiplication:

1. Multiply \(-5x^2\) by \(6x^3\):
\[
-5x^2 \cdot 6x^3 = -30x^{2+3} = -30x^5
\]

2. Multiply \(-5x^2\) by \(-x\):
\[
-5x^2 \cdot (-x) = 5x^{2+1} = 5x^3
\]

3. Multiply \(-5x^2\) by \(2\):
\[
-5x^2 \cdot 2 = -10x^2
\]

Now, combine all these results:

\[
-30x^5 + 5x^3 - 10x^2
\]

So, the final result of the multiplication is:

\[
\boxed{-30x^5 + 5x^3 - 10x^2}
\]