# Determine, with reason, if each statement is true or false. (a) The function {x^4 + x - 1} / {x^3...

## Question:

Determine, with reason, if each statement is true or false.

(a) The function {eq}\displaystyle \dfrac {x^4 + x - 1} {x^3 - 4 x + 9} {/eq} is a proper rational function.

(b) The polynomial {eq}\displaystyle x^3 + 5 x^2 + 4 x {/eq} has only simple, linear factors.

## Factors and Rational Function:

The rational function is defined as the ratio of two functions or polynomials {eq}p(x) {/eq} and {eq}q(x) {/eq}. Where, {eq}q(x)\neq0 {/eq}.

When the degree of a polynomial of the numerator is less than the degree of a polynomial of the denominator, the rational expression is known as a proper rational function.

The linear factor of any polynomial represents as {eq}(x+a) or (x+b) {/eq}.

(a)

The given rational function is:

{eq}\displaystyle \dfrac {x^4 + x - 1} {x^3 - 4 x + 9} {/eq}

Here, the degree of the polynomial of numerator...

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