Question

What is the product of the following two polynomials? (1 point) Responses 8x7+2x6−27x5−18x4 8 x to the 7th power plus 2 x to the 6th power minus 27 x to the 5th power minus 18 x to the 4th power 8x7−22x6−27x5−18x4 8 x to the 7th power minus 22 x to the 6th power minus 27 x to the 5th power minus 18 x to the 4th power 8x7−22x6−27x5+18x4 8 x to the 7th power minus 22 x to the 6th power minus 27 x to the 5th power plus 18 x to the 4th power 8x7+2x6−3x5−18x4

Answer 1

To find the product of the two polynomials given, we first need to identify the two polynomials to be multiplied. Since you haven't provided the specific polynomials yet, let us assume that you are asking about two of the options listed in your response.

For the sake of example, let's say the two polynomials are \( A = 8x^7 + 2x^6 \) and \( B = -27x^5 - 18x^4 \). The product of these two polynomials can be calculated by multiplying each term in the first polynomial by each term in the second polynomial, applying the distributive property.

1. Multiply \( 8x^7 \) by each term in \( B \):
- \( 8x^7 \cdot -27x^5 = -216x^{12} \)
- \( 8x^7 \cdot -18x^4 = -144x^{11} \)

2. Next, multiply \( 2x^6 \) by each term in \( B \):
- \( 2x^6 \cdot -27x^5 = -54x^{11} \)
- \( 2x^6 \cdot -18x^4 = -36x^{10} \)

3. Now combine all the terms:

\[
-216x^{12} + (-144x^{11} - 54x^{11}) - 36x^{10}
\]
Simplifying the coefficients of like terms:
\[
-216x^{12} - 198x^{11} - 36x^{10}
\]

Finally, if you provide the actual two polynomials you want to multiply, I can give you the exact product.