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a. Factor the expression
4n^(2)-12 n-160. Simplify your answer as much as possible, but do not combine like factors.

a. Factor the expression $4 n^{2}-12 n-160$ . Simplify your answer as much as possible, but do not combine like factors.

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Prime factorization

Full solution

Q. a. Factor the expression

4 n^{2}-12 n-160

. Simplify your answer as much as possible, but do not combine like factors.

Identify Common Factor: Step $1$ : Identify the common factor for all terms in the expression $4n^2 - 12n - 160$ . $\newline$ - Common factor is $4$ . $\newline$ - Factor out $4$ : $4(n^2 - 3n - 40)$ .
Factor Quadratic Expression: Step $2$ : Factor the quadratic expression inside the parentheses. $\newline$ - Expression to factor: $n^2 - 3n - 40$ . $\newline$ - Look for two numbers that multiply to $-40$ and add to $-3$ . These numbers are $-8$ and $5$ . $\newline$ - Factorization: $(n - 8)(n + 5)$ .
Write Fully Factored Form: Step $3$ : Write the fully factored form of the original expression. $\newline$ - Combine the extracted common factor and the factored quadratic. $\newline$ - Final factored form: $4(n - 8)(n + 5)$ .

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