Problem 74 - Introductory Algebra for College Students

Question

Factor by grouping. $$x^{3}-3 x^{2}+4 x-12$$

Step-by-Step Solution

Answer

Therefore, the factored form of \(x^{3}-3 x^{2}+4 x-12\) is \((x^{2} + 4)(x - 3)\).

Step 1: Grouping

First, divide the expression into two groups of terms. Therefore, the expression can be divided into ( \(x^{3}-3x^{2}\) ) and ( \(4x-12\) ).

Step 2: Factoring

Within each group, identify and factor out the common factor. This leaves us with \(x^{2}(x - 3) + 4(x - 3)\).

Step 3: Final Factoring

Now, notice that ( \(x - 3\) ) is common to both terms. Factoring out \(x - 3\) from both terms will result in \((x^{2} + 4)(x - 3)\).