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**New York State Regents Exam**Question every day from now until the Regents exams begin next month. At least, that is the plan.### June 2014, Questions 33

**33.** *Write an equation that defines m(x) as a trinomial where m(x) = (3x - 1)(3 - x) + 4x ^{2} + 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 - 3x^{2} - 3 + x = -3x^{2} + 10x - 3

To that, add 4x^{2} + 19.

You get m(x) = x^{2} + 10x + 16. *Don't forget to write it as an equation!*

You needed to find when m(x) = 0, so x^{2} + 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.

Any questions?

If anyone in Brooklyn is looking for an Algebra or Geometry Regents Prep tutor, send me a note. I have a couple of weekly spots available between now and June.

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