Question

Multiply the polynomials (a^2 + 4a - 6) and (3a^2 - a + 3). Simplify the answer.

a) 3a^4 + 12a^3 - 18a^2 - a^3 - 4a^2 + 6a + 9a^2 - 36a + 18
b) 3a^4 + 11a^3 - 13a^2 - 30a + 18
c) 3a^4 + 3a^3 - 7a^2 - 30a - 18
d) 3a^4 + 11a^3 - 18a^2 - 30a + 18

Answer 1

To multiply two polynomials, distribute each term of the first polynomial to every term of the second polynomial and then combine like terms.

Step-by-step explanation:

To multiply the polynomials (a^2 + 4a - 6) and (3a^2 - a + 3), we need to distribute each term of the first polynomial to every term of the second polynomial and then combine like terms.

First, multiply each term of the first polynomial by the second polynomial:

(a^2 + 4a - 6)(3a^2 - a + 3) = 3a^4 + 12a^3 - 18a^2 - a^3 - 4a^2 + 6a + 9a^2 - 36a + 18

Next, combine like terms:

3a^4 + 11a^3 - 13a^2 - 30a + 18