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Factor completely. 2, x, squared, plus, 5, x, minus, 3 2x 2 +5x−3

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Answer
(2x−1)(x+3)\boxed{(2x - 1)(x + 3)}

Multiplying (2x−1)(x+3)(2x - 1)(x + 3) using FOIL results in 2x2+6x−x−32x^2 + 6x - x - 3, which simplifies to the original expression 2x2+5x−32x^2 + 5x - 3.

Problem: Factor the quadratic expression 2x2+5x−32x^2 + 5x - 3.

Steps

  1. Identify the coefficients for the AC method
    Find two numbers that multiply to a⋅c=2⋅(−3)=−6a \cdot c = 2 \cdot (-3) = -6 and add to b=5b = 5. The numbers are 66 and −1-1.
    2x2+6x−1x−32x^2 + 6x - 1x - 3
  2. Factor by grouping
    Group the first two terms and the last two terms.
    2x(x+3)−1(x+3)2x(x + 3) - 1(x + 3)
  3. Factor out the common binomial
    Factor out (x+3)(x + 3) from the expression.
    (2x−1)(x+3)(2x - 1)(x + 3)

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