Factor 9k^2+66k+21

Problem

9*k2+66*k+21

Solution

1. Factor out the greatest common factor (GCF) of the three terms, which is 3

3*(3*k2+22*k+7)

2. Identify the coefficients of the quadratic expression inside the parentheses, a*x2+b*x+c where a=3 b=22 and c=7

3. Find two numbers that multiply to a⋅c=3⋅7=21 and add to b=22 These numbers are 21 and 1

4. Rewrite the middle term 22*k using the two numbers found in the previous step.

3*(3*k2+21*k+1*k+7)

5. Factor by grouping the terms inside the parentheses.

3*((3*k2+21*k)+(k+7))

6. Factor out the common terms from each group.

3*(3*k*(k+7)+1*(k+7))

7. Factor out the common binomial (k+7)

3*(3*k+1)*(k+7)

Final Answer

9*k2+66*k+21=3*(3*k+1)*(k+7)

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