Factor b^2+8b+7

Problem

b2+8*b+7

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=1 b=8 and c=7

2. Find two numbers that multiply to the constant term c=7 and add up to the linear coefficient b=8

3. Determine the factors by testing pairs of numbers that multiply to 7 The only integer pair is 1 and 7

4. Verify that 1 + 7 = 8$, which matches the middle coefficient.

5. Write the expression in its factored form (b+p)*(b+q) using the numbers found.

Final Answer

b2+8*b+7=(b+7)*(b+1)

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