   Chapter 4.S, Problem 1S

Chapter
Section
Textbook Problem

Simplify x 2 − 3 x − 10 x 2 + 9 x + 14 .

To determine

To Find:

The expression by simplifying the given rational expression x23x10x2+9x+14.

Explanation

Approach:

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

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

p(a)k(a)q(a)k(a)=p(a)q(a).

Calculation:

The given rational expression is x23x10x2+9x+14.

Factorise the numerator x23x10.

x23x10=x25x+2x10=x(x5)+2(x5)=(x5)(x+2)

Factorise the denominator x2+9x+14

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