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Factor. $\newline$ $10v^2 + 40v - 50$

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Factor quadratics

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Q. Factor.

\newline

10v^2 + 40v - 50

Identify Common Factor: First, look for a common factor in all terms. $10v^2 + 40v - 50$ can be divided by $10$ .
Divide by Common Factor: Divide each term by $10$ . $10v^2 \div 10 = v^2$ , $40v \div 10 = 4v$ , $-50 \div 10 = -5$ . So, $10v^2 + 40v - 50 = 10(v^2 + 4v - 5)$ .
Factor Quadratic Expression: Now, factor the quadratic $v^2 + 4v - 5$ . We need two numbers that multiply to $-5$ and add to $4$ .
Find Correct Numbers: The numbers are $5$ and $-1$ because $5 \times -1 = -5$ and $5 + (-1) = 4$ .
Write Factored Form: Write the factored form using these numbers. $\newline$ $v^2 + 4v - 5 = (v + 5)(v - 1)$ .
Reintroduce Common Factor: Now, put the common factor $10$ back in. $\newline$ $10(v^2 + 4v - 5) = 10(v + 5)(v - 1)$ .

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