Factor x^2-14x+40

Problem

x2−14*x+40

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=1 b=−14 and c=40

2. Find two numbers that multiply to c (40 and add to b (−14.

3. Determine the factors of 40 that satisfy the condition. Since the sum is negative and the product is positive, both numbers must be negative. The numbers are −4 and −10 because (−4)×(−10)=40 and (−4)+(−10)=−14

4. Write the expression in factored form (x+p)*(x+q) using the numbers found.

Final Answer

x2−14*x+40=(x−4)*(x−10)

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