Factor 4x^2+7x-15

Problem

4*x2+7*x−15

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=4 b=7 and c=−15

2. Find two numbers that multiply to a⋅c=4⋅(−15)=−60 and add to b=7

3. Determine the factors of −60 that satisfy the condition: the numbers are 12 and −5 because 12⋅(−5)=−60 and 12 + (-5) = 7$.

4. Rewrite the middle term 7*x using these two numbers: 4*x2+12*x−5*x−15

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

6. Factor out the common binomial (x+3) to obtain the final factored form.

Final Answer

4*x2+7*x−15=(4*x−5)*(x+3)

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