Factor. $\newline$ $x^{2}+14 x+48$ $\newline$ Answer:

Full solution

Q. Factor.

\newline

x^{2}+14 x+48

\newline

Answer:

Identify Structure: Identify the structure of the quadratic expression. $\newline$ The given expression is a quadratic in the form of $ax^2 + bx + c$ , where $a = 1$ , $b = 14$ , and $c = 48$ .
Find Numbers: Look for two numbers that multiply to $ac$ ( $a*c$ ) and add up to $b$ . In this case, $ac = 1*48 = 48$ and $b = 14$ . We need to find two numbers that multiply to $48$ and add up to $14$ .
Determine Factors: Find the two numbers. $\newline$ The numbers that multiply to $48$ and add up to $14$ are $6$ and $8$ , since $6 \times 8 = 48$ and $6+8 = 14$ .
Factor by Grouping: Write the expression using the two numbers found. $\newline$ The expression can be rewritten as $x^2 + 6x + 8x + 48$ .
Factor Common Factors: Factor by grouping. $\newline$ Group the terms to factor by common factors: $(x^2 + 6x) + (8x + 48)$ .
Write Final Form: Factor out the common factors from each group. $\newline$ From the first group, factor out $x$ : $x(x + 6)$ . $\newline$ From the second group, factor out $8$ : $8(x + 6)$ .
Write Final Form: Factor out the common factors from each group. $\newline$ From the first group, factor out $x$ : $x(x + 6)$ . $\newline$ From the second group, factor out $8$ : $8(x + 6)$ .Write the final factored form. $\newline$ Since both groups contain the factor $(x + 6)$ , the expression can be factored as $(x + 6)(x + 8)$ .