Q. Factor the quadratic expression completely.15x2−4x−4=
Identify Coefficients: Step Title: Identify the CoefficientsConcise Step Description: Identify the coefficients of the quadratic expression, which are the numbers in front of the variables. In this case, the coefficients are 15, −4, and −4.Step Calculation: Coefficients are 15, −4, −4Step Output: Coefficients: 15, −4, −4
Find Factors: Step Title: Find the FactorsConcise Step Description: Find two numbers that multiply to the product of the first and last coefficients 15×−4=−60 and add to the middle coefficient −4.Step Calculation: Factors of −60 that add up to −4 are −10 and 6.Step Output: Factors: −10, 6
Rewrite Middle Term: Step Title: Rewrite the Middle TermConcise Step Description: Rewrite the middle term using the factors found in the previous step.Step Calculation: 15x2−10x+6x−4Step Output: Rewritten Expression: 15x2−10x+6x−4
Factor by Grouping: Step Title: Factor by GroupingConcise Step Description: Group the terms into two pairs and factor out the greatest common factor from each pair.Step Calculation: (15x2−10x)+(6x−4)=5x(3x−2)+2(3x−2)Step Output: Factored by Grouping: 5x(3x−2)+2(3x−2)
Factor Out Common Binomial Factor: Step Title: Factor Out the Common Binomial FactorConcise Step Description: Factor out the common binomial factor from the grouped terms.Step Calculation: (5x+2)(3x−2)Step Output: Factored Form: (5x+2)(3x−2)