Factor 4x^2+4x-15

Problem

4*x2+4*x−15

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=4 b=4 and c=−15

2. Find two numbers that multiply to a⋅c=4⋅(−15)=−60 and add to b=4

3. Determine the pair of numbers, which are 10 and −6

4. Rewrite the middle term 4*x using the two numbers found: 10*x−6*x

4*x2+10*x−6*x−15

5. Factor by grouping by taking the greatest common factor out of the first two terms and the last two terms.

2*x*(2*x+5)−3*(2*x+5)

6. Factor out the common binomial (2*x+5)

(2*x−3)*(2*x+5)

Final Answer

4*x2+4*x−15=(2*x−3)*(2*x+5)

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