Factor 7x^2-32x-60

Problem

7*x2−32*x−60

Solution

1. Identify the coefficients of the quadratic expression a*x2+b*x+c where a=7 b=−32 and c=−60

2. Find two numbers that multiply to a⋅c=7⋅(−60)=−420 and add to b=−32

3. Determine the pair of numbers by testing factors of −420 The numbers are −42 and 10 because:

−42⋅10=−420

−42+10=−32

4. Rewrite the middle term −32*x using the two numbers found:

7*x2−42*x+10*x−60

5. Factor by grouping the first two terms and the last two terms:

7*x*(x−6)

10*(x−6)

6. Factor out the common binomial (x−6)

(7*x+10)*(x−6)

Final Answer

7*x2−32*x−60=(7*x+10)*(x−6)

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