Chapter 4.1, Problem 49PS

### Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
ISBN: 9781285195728

Chapter
Section

### Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
ISBN: 9781285195728
Textbook Problem

# For Problems 9-50, simplify each rational expression. (Objective 2) − 40 x 3 + 24 x 2 + 16 x 20 x 3 + 28 x 2 + 8 x

To determine

To Find:

The expression by simplifying the given rational expression.

Explanation

Approach:

A rational expression is defined as the quotient obtained by a division of two polynomials in the form of p(x)q(x) where p(x) and q(x) are polynomials in such a way that the variable x does not assume values such that q(x)=0.

For values of x where q(x) and k(x) are both nonzero expressions, then by the fundamental principle of fractions, for all polynomials p(x), the following holds.

p(x)â‹…k(x)q(x)â‹…k(x)=p(x)q(x).

Calculation:

The given rational expression is âˆ’40x3+24x2+16x20x3+28x2+8x.

Factorise the numerator âˆ’40x3+24x2+16x.

âˆ’40x3+24x2+16x=âˆ’8x(5x2âˆ’3xâˆ’2)=âˆ’8x(5x2âˆ’5x+2xâˆ’2)=âˆ’8x{5x(xâˆ’1)+2(xâˆ’1)}=âˆ’8x(5x+2)(xâˆ’1)

Factorise the denominator 20x3+28x2+8x.

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