Factor w^2+30w+81

Problem

w2+30*w+81

Solution

1. Identify the coefficients of the quadratic expression in the form a*w2+b*w+c where a=1 b=30 and c=81

2. Find two numbers that multiply to c (81) and add up to b (30).

3. List the factor pairs of 81: (1,81) (3,27) and (9,9)

4. Select the pair (3,27) because 3×27=81 and 3 + 27 = 30$.

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

Final Answer

w2+30*w+81=(w+3)*(w+27)

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