Question
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Answer
\( c^{2}+11c+18 = (c+2)(c+9) \)
Solution
Factor the expression \( c^{2}+11c+18 \).
Factor the expression by following steps:
- step0: Factor:
\(c^{2}+11c+18\)
- step1: Rewrite the expression:
\(c^{2}+\left(9+2\right)c+18\)
- step2: Calculate:
\(c^{2}+9c+2c+18\)
- step3: Rewrite the expression:
\(c\times c+c\times 9+2c+2\times 9\)
- step4: Factor the expression:
\(c\left(c+9\right)+2\left(c+9\right)\)
- step5: Factor the expression:
\(\left(c+2\right)\left(c+9\right)\)
The fully factored form of \(c^{2}+11c+18\) is \((c+2)(c+9)\).
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Simplify this solution Bonus Knowledge
To fully factorize the expression \( c^{2}+11c+18 \), we need to find two numbers that multiply to 18 (the constant term) and add up to 11 (the coefficient of \( c \)). Those numbers are 2 and 9. This means we can rewrite the expression as \( (c + 2)(c + 9) \). So, the fully factorized form is \( (c + 2)(c + 9) \). Happy factoring!
