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Dana Henson
Mathematics
13 April, 04:44
Factor the trinomial f (x) = 2x² + 5x - 12?
+5
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Slade
13 April, 05:06
0
(x + 4) (2x - 3)
Step-by-step explanation:
Given
f (x) = 2x² + 5x - 12
Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x - term.
product = 2 * - 12 = - 24 and sum = + 5
The factors are + 8 and - 3
Use these factors to split the x - term
2x² + 8x - 3x - 12 (factor the first/second and third/fourth terms)
2x (x + 4) - 3 (x + 4) ← factor out (x + 4) from each term
(x + 4) (2x - 3)
Thus
f (x) = 2x² + 5x - 12 = (x + 4) (2x - 3) ← in factored form
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