Factor x^2+18x+77

Problem

x2+18*x+77

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=1 b=18 and c=77

2. Find two numbers that multiply to c (77 and add to b (18.

3. Determine the factors of 77 by testing pairs: 1×77 (sum is 78 and 7×11 (sum is 18.

4. Select the pair 7 and 11 since 7×11=77 and 7 + 11 = 18$.

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

Final Answer

x2+18*x+77=(x+7)*(x+11)

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