Question

What is the product of the following polynomials: (−3x5−4x4)(7x2−2x+6)
?(1 point)
(−3x5−4x4)(7x2−2x+6)=

Answer 1

To find the product of the polynomials \( (-3x^5 - 4x^4)(7x^2 - 2x + 6) \), we will multiply each term in the first polynomial by each term in the second polynomial.

1. **Distributing \(-3x^5\)**:
- \(-3x^5 \cdot 7x^2 = -21x^7\)
- \(-3x^5 \cdot (-2x) = 6x^6\)
- \(-3x^5 \cdot 6 = -18x^5\)

2. **Distributing \(-4x^4\)**:
- \(-4x^4 \cdot 7x^2 = -28x^6\)
- \(-4x^4 \cdot (-2x) = 8x^5\)
- \(-4x^4 \cdot 6 = -24x^4\)

Now we combine all the results:
\[
(-3x^5 - 4x^4)(7x^2 - 2x + 6) = -21x^7 + 6x^6 - 18x^5 - 28x^6 + 8x^5 - 24x^4
\]

Next, we can combine like terms:
- For \(x^7\): \(-21x^7\)
- For \(x^6\): \(6x^6 - 28x^6 = -22x^6\)
- For \(x^5\): \(-18x^5 + 8x^5 = -10x^5\)
- For \(x^4\): \(-24x^4\)

Putting it all together, the product is:
\[
-21x^7 - 22x^6 - 10x^5 - 24x^4
\]

Thus, the final answer is:
\[
\boxed{-21x^7 - 22x^6 - 10x^5 - 24x^4}
\]