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Chapter 5: Problem 96

Factor. $$c^{2}-9 c+8$$

Short Answer

Expert verified
The factored form of \(c^{2}-9 c+8\) is \((c-1)(c-8)\).

Step by step solution

01

Identify the Coefficients and Constant

The coefficient of \(c^{2}\) is 1, the coefficient of \(c\) is -9, and the constant term is 8.
02

Find Two Numbers that Multiply to 8 and Add to -9

The two numbers that satisfy this condition are -1 and -8, since -1 multiplied by -8 gives 8, and -1 plus -8 equals -9.
03

Split the Middle Term

Express the middle term (-9c) as the sum of -1c and -8c. This gives \(c^{2}-1 c-8 c + 8\).
04

Group and Factor

Group the terms to get \((c^{2}-1 c) - (8 c - 8)\). Factoring out a \(c\) from the first group and a -8 from the second gives \(c(c-1) - 8(c-1)\).
05

Factor the Common Binomial

The expression \(c(c-1) - 8(c-1)\) has a common binomial of \((c-1)\), factoring this gives \((c-1)(c-8)\), which is the factored form of the original expression.

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