Problem 91 - Introductory Algebra for College Students

Question

Factor each polynomial. $$4 x^{5}(x+1)-6 x^{3}(x+1)-8 x^{2}(x+1)$$

Step-by-Step Solution

Answer

The factored form of the polynomial is therefore \((x+1)(4x^{5}-6x^{3}-8x^{2})\).

Step 1: Identify Common Factors

The first step here is to identify any common factors among the given terms. Noticing that each term contains the factor \(x+1\).

Step 2: Extract Common Factors

The next step is to 'take out' or extract this common factor from each term. So for each term, divide by the common factor \(x+1\). Our polynomial is then the product of this common factor and the resulting expression, which is: \(4x^{5}-6x^{3}-8x^{2}\).

Step 3: Express the Polynomial

Now rewrite the polynomial expression as the product of the common factor and the new polynomial obtained in the previous step: \((x+1)(4x^{5}-6x^{3}-8x^{2})\).