Daily Regents: Trinomials

I'll be reviewing a 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) + 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.

Any questions?

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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.