Factor 8x^2-14x-15

Problem

8*x2−14*x−15

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=8 b=−14 and c=−15

2. Calculate the product of a and c which is 8×−15=−120

3. Find two numbers that multiply to −120 and add to the middle coefficient b=−14 These numbers are −20 and 6

4. Rewrite the middle term −14*x using the two numbers found: 8*x2−20*x+6*x−15

5. Factor by grouping the first two terms and the last two terms: 4*x*(2*x−5)+3*(2*x−5)

6. Factor out the common binomial (2*x−5) to obtain the final factored form.

Final Answer

8*x2−14*x−15=(4*x+3)*(2*x−5)

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