Problem 114
Question
Factor completely. $$12 x^{2}(x-1)-4 x(x-1)-5(x-1)$$
Step-by-Step Solution
Verified Answer
The fully factored expression is \((x-1)(12x^2 - 4x - 5)\)
1Step 1: Identify the common factor
In the given expression, the common factor amongst all terms is \( (x-1) \).
2Step 2: Factor by Grouping
Pull out the common factor from each term. The expression becomes \((x-1)(12x^2 - 4x - 5)\).
3Step 3: Factor the Quadratic
Next, factor the quadratic expression \(12x^2 - 4x - 5\). This does not factor nicely, so regard it as simply a part of the fully factored expression.
Other exercises in this chapter
Problem 113
Explain why \(x^{2}-1\) is factorable, but \(x^{2}+1\) is not.
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Solve the system: $$\left\\{\begin{array}{c}4 x-y=105 \\\x+7 y=-10\end{array}\right.$$
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Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. \(-4 x^{2}+12 x\) can be
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Explain how to factor \(x^{3}+1\)
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