Factor x^2+8x+12

Problem

$x^2+8x+12$

Solution

1. Identify the coefficients of the quadratic expression in the form $a{x}^2+bx+c$ where $a=1$ $b=8$ and $c=12$

2. Find two numbers that multiply to the constant term $c=12$ and add up to the linear coefficient $b=8$

3. Determine the factors of $12$ $(1,12)$ $(2,6)$ and $(3,4)$

4. Select the pair $(2,6)$ because $2\times 6=12$ and $\mathrm{\$}2$ + 6 = 8$.

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

Final Answer

$x^2+8x+12=(x+2)(x+6)$

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