Question

Multiply.

1) (3t^2 - 2t - 4) * (5t + 9)

Writing.

1) Explain why the product of a quadratic polynomial and a linear polynomial must be a cubic polynomial.

Answer 1

(3t^2 - 2t - 4) * (5t + 9)

Multiply each term in one set of parentheses by each term in the other set of parentheses.

3t^2(5t + 9) - 2t(5t + 9) - 4(5t + 9)
15t^3 + 27t^2 - 10t^2 - 18t - 20t - 36

combine like terms
15t^3 + (27t^2 - 10t^2) + (- 18t - 20t) - 36

15t^3 + 17t^2 -38t - 36


A quadratic has a power of 2 as its highest exponent, and a linear has a power of 1 as its highest exponent. When those highest exponents are multiplied together, they will result in a highest exponent of 2 + 1 = 3.