Write an equation that defines m (x) as a trinomial where m (x) = (3x-1) (3-x) + 4x^2+18

m (x) = x² + 10x + 15

Step-by-step explanation:

Rewrite m (x) = (3x-1) (3-x) + 4x² + 18 as a trinomial (three-term equation) by simplifying the equation. Expand the brackets by multiplying the binomials and collect like terms.

m (x) = (3x-1) (3-x) + 4x² + 18 Multiply brackets with terms FOIL (first, outside, inside, last)

m (x) = (9x - 3x² - 3 + x) + 4x² + 18 The brackets can be removed

m (x) = 9x - 3x² - 3 + x + 4x² + 18 See what terms have the same variables

m (x) = - 3x² + 4x² + 9x + x + 18 - 3 Like terms are rearranged together

m (x) = x² + 10x + 15 Collected like terms