8th Grade Algebra
posted by Bridget on .
1) (3t^2 - 2t - 4) * (5t + 9)
1) Explain why the product of a quadratic polynomial and a linear polynomial must be a cubic polynomial.
(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.