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To solve factors of 2a2 + a - 15, use these steps:
1) What are the factors of 2a2? The choices are 2a2 x 1 and 2a x a
2) What are the factors of 15? The choices are 1x15 and 3x5.
We can setup the factors to look like this:
(A ± B) * (C ± D)
Because the last term in the expression is negatie (-15), the signs must be opposite. Therefore:
(A + B) * (C - D)
Since the middle term is positive, the product of B*C (which is positive) must be greater than the product of A*D (which is negative).
At this point, you simply need to guess and check the possibilities. Substitute 2a and a (from step 1) for A and C, and 3 and 5 (from step 2) for B and D to yield:
(2a - 5) * (a + 3)
Therefore, the factos of 2a2 + a - 15 are (2a - 5) and (a + 3)