Factor x^2+10x+21

Problem

x2+10*x+21

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=1 b=10 and c=21

2. Find two numbers that multiply to c (21) and add to b (10).

3. Determine the factors by testing pairs of numbers that multiply to 21: 1 and 21, or 3 and 7.

4. Select the pair 3 and 7, because 3 + 7 = 10$.

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

Final Answer

x2+10*x+21=(x+3)*(x+7)

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