Factor completely.3, x, squared, plus, 5, x, minus, 23x 2 +5x−2
Question
Factor completely.3, x, squared, plus, 5, x, minus, 23x 2 +5x−2
Solution
The expression you provided seems to be a bit unclear. However, if you're asking to factor the quadratic equation 3x^2 + 5x - 2, here are the steps:
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Write down the quadratic equation: 3x^2 + 5x - 2 = 0
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Identify the coefficients a, b, and c in the standard form of the quadratic equation ax^2 + bx + c = 0. In this case, a = 3, b = 5, and c = -2.
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Find two numbers that multiply to give ac (a times c), and add to give b. In this case, ac = 3*(-2) = -6 and b = 5. The numbers that satisfy this are 2 and -3, because 2*(-3) = -6 and 2 + (-3) = -1.
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Rewrite the equation by splitting the middle term using the two numbers found in step 3: 3x^2 + 2x - 3x - 2 = 0
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Factor by grouping: x(3x + 2) - 1(3x + 2) = 0
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Since the terms in parentheses are the same, you can factor them out: (3x + 2)(x - 1) = 0
So, the factored form of the equation 3x^2 + 5x - 2 = 0 is (3x + 2)(x - 1) = 0.
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