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$X^2/12-2x/3-4$

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Factor by grouping

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Q.

X^2/12-2x/3-4

Find Common Denominator: Find a common denominator for the terms in the expression. $\newline$ The common denominator for the terms $X^2/12$ , $-2x/3$ , and $-4$ is $12$ . We will rewrite each term with the common denominator of $12$ . $\newline$ $X^2/12$ stays the same since its denominator is already $12$ . $\newline$ $-2x/3$ is multiplied by $4/4$ to get $-8x/12$ . $\newline$ $-4$ is multiplied by $-2x/3$ $1$ to get $-2x/3$ $2$ .
Rewrite with Common Denominator: Rewrite the expression with the common denominator. $\newline$ Now that we have a common denominator, we can combine the terms into a single fraction: $\newline$ $(X^2 - 8x - 48) / 12$
Factor Numerator: Factor the numerator. $\newline$ We need to factor the quadratic expression $X^2 - 8x - 48$ . To do this, we look for two numbers that multiply to $-48$ and add to $-8$ . These numbers are $-12$ and $+4$ . $\newline$ So, we can write the numerator as $(X - 12)(X + 4)$ .
Write Factored Expression: Write the factored form of the entire expression. $\newline$ Now that we have factored the numerator, we can write the factored form of the entire expression as: $\newline$ $\frac{(X - 12)(X + 4)}{12}$

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