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Factor. $\newline$ $q^2 + 22q - 23$

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Factor quadratics

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Q. Factor.

\newline

q^2 + 22q - 23

Identify Quadratic Trinomial Form: Identify the quadratic trinomial form, which is $ax^2 + bx + c$ .
Find Multiplying and Adding Numbers: Look for two numbers that multiply to $-23$ (the $c$ term) and add up to $22$ (the $b$ term).
Determine Numbers: Multiply and Add: The numbers are $23$ and $-1$ because $23 \times -1 = -23$ and $23 + (-1) = 22$ .
Rewrite Middle Term: Rewrite the middle term using the two numbers found: $q^2 + 23q - 1q - 23$ .
Factor by Grouping: Factor by grouping: $(q^2 + 23q) - (1q + 23)$ .
Factor Out Common Factor: Factor out the common factor from each group: $q(q + 23) - 1(q + 23)$ .
Factor Out Common Binomial: Factor out the common binomial: $(q - 1)(q + 23)$ .

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