Factor x^2+17x+72

Problem

x2+17*x+72

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=1 b=17 and c=72

2. Find two numbers that multiply to c (72 and add up to b (17.

3. List the factor pairs of 72 (1,72) (2,36) (3,24) (4,18) (6,12) and (8,9)

4. Select the pair (8,9) because 8×9=72 and 8 + 9 = 17$.

5. Write the factored form using these two numbers as (x+p)*(x+q)

Final Answer

x2+17*x+72=(x+8)*(x+9)

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