Problem 89 - Introductory Algebra for College Students

Question

Factor each polynomial. $$x^{3}-4+3 x^{3} y-12 y$$

Step-by-Step Solution

Answer

The factored form of the given polynomial \(x^{3}-4+3 x^{3} y-12 y\) is \((x^{3} - 4)(1 + 3y)\).

Step 1: Organize the polynomial

Rearrange the expression in a way that similar terms are together. It will give us: \(x^{3}(1 + 3y) - 4(1 + 3y)\).

Step 2: Factoring the polynomial

Next, look for common factors in all the terms. Here, \(1 + 3y\) is a common factor. So, one can factor out \(1 + 3y\) from the polynomial. This gives us: \((x^{3} - 4)(1 + 3y)\).