Factor x^2+14x+24

Problem

x2+14*x+24

Solution

1. Identify the coefficients of the quadratic expression in the form a*x2+b*x+c where a=1 b=14 and c=24

2. Find two numbers that multiply to c (24 and add to b (14.

3. List factors of 24 to find the pair: 1⋅24 (sum 25, 3⋅8 (sum 11, 4⋅6 (sum 10, and 2⋅12 (sum 14.

4. Select the pair 2 and 12 since 2⋅12=24 and 2 + 12 = 14$.

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

Final Answer

x2+14*x+24=(x+2)*(x+12)

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