Answer:
2(3x -1)(2x +3) = 0
Explanation:
A graphing calculator can often provide useful help in discovering the real factors of polynomials.
We presume you want to factor the standard form equation ...
12x^2 +14x -6 = 0 . . . . . subtract 18 from both sides
2(6x^2 +7x -3) = 0 . . . . factor out the common factor
2(6x^2 +9x -2x -3) = 0 . . . . split the middle term to aid factoring
2(3x(2x +3) -1(2x +3)) = 0 . . . . factor pairs of terms
2(3x -1)(2x +3) = 0 . . . . . factored standard form equation
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Additional comments
The calculator graph shows the zeros are rational and have values -3/2 and 1/3. A zero of x=p means (x -p) is a factor. Translated to factors without fractions, these would be ...
(x +3/2) ⇒ (2x +3) and (x -1/3) ⇒ (3x -1)
The only remaining job is to find the additional factor that makes the leading coefficient be 12 instead of (2)(3) = 6.
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When factoring 6x^2 +7x -3, we're looking for two numbers that have a sum of +7 and a product of (6)(-3) = -18. The factors we need are 9 and -2, which are the values we use when we split the middle term: 7x ⇒ 9x -2x.
We choose to do the factoring this way because it is straightforward and relatively easy to explain. There are other methods used when the leading coefficient is not 1, but they can be more difficult to explain.