June 2014, Questions 33
33. Write an equation that defines m(x) as a trinomial where m(x) = (3x - 1)(3 - x) + 4x2 + 19. Solve for x when m(x) = 0.
You need to multiply the binomials and then combine all the like terms.
(3x - 1)(3 - x) = 9x - 3x2 - 3 + x = -3x2 + 10x - 3
To that, add 4x2 + 19.
You get m(x) = x2 + 10x + 16. Don't forget to write it as an equation!
You needed to find when m(x) = 0, so x2 + 10x + 16 = 0. That's a simple quadratic equation to solve. What two factors of 16 add up to 10? That's 8 and 2.
So (x + 8)(x + 2) = 0
x + 8 = 0 or x + 2 = 0
Then x = -8 or x = -2.
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