Factor $18v^{2}-15v-18$

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Q. Factor

18v^{2}-15v-18

Identify Coefficients: Step Title: Identify the Coefficients $\newline$ Concise Step Description: Identify the coefficients of the quadratic equation, which are the numbers in front of the variables. In this case, the coefficients are $18$ , $-15$ , and $-18$ . $\newline$ Step Calculation: Coefficients are $18$ , $-15$ , $-18$ $\newline$ Step Output: Coefficients: $18$ , $-15$ , $-18$
Find Factors: Step Title: Find the Factors $\newline$ Concise Step Description: Find two numbers that multiply to the product of the first and last coefficients $18 \times -18 = -324$ and add to the middle coefficient $-15$ . $\newline$ Step Calculation: Factors of $-324$ that add up to $-15$ are $-27$ and $12$ . $\newline$ Step Output: Factors: $-27$ , $12$
Rewrite Middle Term: Step Title: Rewrite the Middle Term $\newline$ Concise Step Description: Rewrite the middle term using the factors found in the previous step. $\newline$ Step Calculation: $18v^2 - 27v + 12v - 18$ $\newline$ Step Output: Rewritten quadratic: $18v^2 - 27v + 12v - 18$
Factor by Grouping: Step Title: Factor by Grouping $\newline$ Concise Step Description: Group the terms into two pairs and factor out the common factors from each pair. $\newline$ Step Calculation: $18v^2 - 27v$ + $12v - 18$ = $9v(2v - 3)$ + $6(2v - 3)$ $\newline$ Step Output: Grouped factors: $9v(2v - 3)$ + $6(2v - 3)$
Factor Out Common Binomial: Step Title: Factor Out the Common Binomial $\newline$ Concise Step Description: Factor out the common binomial factor from the grouped terms. $\newline$ Step Calculation: $(9v + 6)(2v - 3)$ $\newline$ Step Output: Factored Form: $(9v + 6)(2v - 3)$