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Chapter 6: Problem 91

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

Short Answer

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

Step by step solution

01

Identify Common Factors

The first step here is to identify any common factors among the given terms. Noticing that each term contains the factor \(x+1\).
02

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: \(4x^{5}-6x^{3}-8x^{2}\).
03

Express the Polynomial

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

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