Factor x^2-14x+48

Problem

x2−14*x+48

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=1 b=−14 and c=48

2. Find two numbers that multiply to c (48 and add up to b (−14.

3. Determine the factors of 48 that satisfy the condition. Since the product is positive and the sum is negative, both numbers must be negative. The pairs are (−1,−48) (−2,−24) (−3,−16) (−4,−12) and (−6,−8)

4. Select the pair (−6,−8) because −6+(−8)=−14

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

Final Answer

x2−14*x+48=(x−6)*(x−8)

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