SolveMathAI

Factor 6x^2 + 11x - 10

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Answer
(3x−2)(2x+5)\boxed{(3x - 2)(2x + 5)}

Expanding the factored form yields 6x2+15x−4x−10=6x2+11x−106x^2 + 15x - 4x - 10 = 6x^2 + 11x - 10, confirming the result.

Problem: Factor the quadratic expression 6x2+11x−106x^2 + 11x - 10.

Steps

  1. Find two numbers that multiply to 6⋅(−10)=−606 \cdot (-10) = -60 and add to 1111
    The numbers are 15 and −4\text{The numbers are } 15 \text{ and } -4
  2. Rewrite the middle term using these two numbers
    6x2+15x−4x−106x^2 + 15x - 4x - 10
  3. Factor by grouping
    3x(2x+5)−2(2x+5)3x(2x + 5) - 2(2x + 5)
  4. Factor out the common binomial
    (3x−2)(2x+5)(3x - 2)(2x + 5)

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