SOLUTION: factor the trinomial a^2-2af-35f2 the answer is?

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Question 426805: factor the trinomial
a^2-2af-35f2
the answer is?
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
I assume that last 2 is an exponent:
a%5E2-2af-35f%5E2
When factoring, always start with the Greatest Common Factor (GCF). The GCF here is 1 and we don't normally factor out 1's.

Next look to the other methods of factoring:
  • Patterns
    • a%5E2-b%5E2+=+%28a%2Bb%29%28a-b%29
    • a%5E2%2B2ab%2Bb%5E2+=+%28a%2Bb%29%28a%2Bb%29+=+%28a%2Bb%29%5E2
    • a%5E2-2ab%2Bb%5E2+=+%28a-b%29%28a-b%29+=+%28a-b%29%5E2
    • a%5E3%2Bb%5E3+=+%28a%2Bb%29%28a%5E2-ab%2Bb%5E2%29
    • a%5E3-b%5E3+=+%28a-b%29%28a%5E2%2Bab%2Bb%5E2%29
  • Trinomials
  • Factoring by grouping
  • Factoring by trial and error of the rational roots

Your expression does not fit any of the patterns. But it is a trinomial. And it is a trinomial with a leading coefficient of 1, the easiest kind of trinomial to factor. To factor this we ask ourselves: "Are there factors of -35f%5E2 (the term at the end) that add up to -2f (the coefficient in the middle)? Answer: Yes, -7f and 5f are factors of -35f%5E2 that add up to -2f. So this trinomial will factor:
(a-7f)(a+2f)
These factors will not factor further so we are finished.