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Choose two trinomials from the list below to factor. Using complete sentences, explain how to factor each one. Be sure that the final factorization (or "answer") is a part of your explanation. 2x2 + 13x + 15 2x2 + 27x + 13 5x2 − 2x − 7 10x2 − 7x − 3 8x2 − 11x + 3
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Use a technique called ac test where a is the coefficient of x^2 term and c is the constant term. Take the first trinomial as an example. Factor a or 2 into 2 factors as 2 and 1, then factor 15 into 2 factors as 3 and 5. We have 2 3 1 5 Calculate the cross product that is 2x5 + 1x3 = 13. Since the result matches coefficient b or 13, we have found the 4 numbers we need. We then write (2x + 3)(x +5) Take another example - the second one. Factor 2 into 2 and 1, 13 into 1 and 13 2 1 1 13 Verify that 2x13 + 1x1 = 27. (2x + 1)(x + 13) There are several ways to factor the above trinomials.
5x^2 - 2x - 7 5 -7 1 1 5x1 + 1x(-7) = 2 (5x - 7)(x + 1)
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