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Factor the quadratic expression completely.

15x^(2)-4x-4=

Factor the quadratic expression completely.\newline15x24x4=15x^{2}-4x-4=

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Q. Factor the quadratic expression completely.\newline15x24x4=15x^{2}-4x-4=
  1. Identify Coefficients: Step Title: Identify the Coefficients\newlineConcise Step Description: Identify the coefficients of the quadratic expression, which are the numbers in front of the variables. In this case, the coefficients are 1515, 4-4, and 4-4.\newlineStep Calculation: Coefficients are 1515, 4-4, 4-4\newlineStep Output: Coefficients: 1515, 4-4, 4-4
  2. Find Factors: Step Title: Find the Factors\newlineConcise Step Description: Find two numbers that multiply to the product of the first and last coefficients 15×4=6015 \times -4 = -60 and add to the middle coefficient 4 -4.\newlineStep Calculation: Factors of 60 -60 that add up to 4 -4 are 10 -10 and 66.\newlineStep Output: Factors: 10 -10, 66
  3. Rewrite Middle Term: Step Title: Rewrite the Middle Term\newlineConcise Step Description: Rewrite the middle term using the factors found in the previous step.\newlineStep Calculation: 15x210x+6x415x^2 - 10x + 6x - 4\newlineStep Output: Rewritten Expression: 15x210x+6x415x^2 - 10x + 6x - 4
  4. Factor by Grouping: Step Title: Factor by Grouping\newlineConcise Step Description: Group the terms into two pairs and factor out the greatest common factor from each pair.\newlineStep Calculation: (15x210x)+(6x4)=5x(3x2)+2(3x2)(15x^2 - 10x) + (6x - 4) = 5x(3x - 2) + 2(3x - 2)\newlineStep Output: Factored by Grouping: 5x(3x2)+2(3x2)5x(3x - 2) + 2(3x - 2)
  5. Factor Out Common Binomial Factor: Step Title: Factor Out the Common Binomial Factor\newlineConcise Step Description: Factor out the common binomial factor from the grouped terms.\newlineStep Calculation: (5x+2)(3x2)(5x + 2)(3x - 2)\newlineStep Output: Factored Form: (5x+2)(3x2)(5x + 2)(3x - 2)