Larry P.

asked • 07/19/16

Finding Missing Term on Factored Trinomial or Polynomial

How could I find out the missing term in these examples
1) __x2-9x-9 = (__x+3)(x-3)
2) __x2-19x-20 = (__x+5)(x-4)
3) __x2-17x-5 = (3x-5)(__x+1)
Please show me the complete and clear solutions. Thanks in advance.

Katharyn F.

Hi Larry,
It helps to multiply out with a coefficient of 1 first to see how that answer compares with the one required.
So for problem 1) (x+3)(x-3)=x2-9. So we are missing the -9x in the middle. To get this, we can first try adding a coefficient of 2. Then we get 2x2-6x+3x-9. That won't work, but we see now what we need: we need to have -12x+3x=9x. The 3x is a given, as there is no possible coefficient that could change this when multiplying out. However, we can change the coefficient in front of the first x so that we get -12x.
The answer should then be (4x+3)(x-3)=4x2-12x+3x-9=4x2-9x-9, and we have our first solution.
Problem 2) can be solved similarly. Try multiplying out, and we see we need to have -24x+5x in the middle to get our -19x. To achieve this, we need to add a coefficient of 6 in the blank space.
That is, the answer will be (6x+5)(x-4)=6x2-24x+5x-20=6x2-19x-20.
Problem 3) is a little trickier but can be solved similarly. Multiplying out and calling the missing coefficient N, we have 3Nx2-5Nx+3x-5. So -5Nx+3x must be equal to -17x. So N must be 4, given that -20x+3x=-17x. 
Our answer is thus (3x-5)(4x+1)=12x2-17x-5.
I hope this helps, and find me on WyzAnt if you are interested in private tutoring :-)


2 Answers By Expert Tutors


Kenneth S. answered • 07/19/16

4.8 (62)

Algebra II EXPERT will help you survive & prosper

Larry P.

Could you show me the steps visually like
STEP 1) (ax+3)(x-3)
again, thanks


Mack M. answered • 07/19/16

New to Wyzant

Math, Economics, Poli-Sci, & Writing

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