Respuesta :

WojtekR
Excluded values are -3, 0 and 8, so denominator will be:

[tex](x-(-3))\cdot(x-0)\cdot(x-8)=(x+3)\cdot x\cdot(x-8)=(x+3)(x-8)x=\\\\=(x^2-8x+3x-24)x=(x^2-5x-24)x=\boxed{x^3-5x^2-24x}[/tex]

Answer A.

Answer:

The correct option is 1.

Step-by-step explanation:

If a rational function is defined as

[tex]R(x)=\frac{P(x)}{Q(x)}[/tex]

then the excluded values of a rational expression are zeroes of the denominator. In other words, the excluded values of a rational expression are those values of x for which Q(x)=0.

It is given that the excluded values of a rational expression are –3, 0, and 8. It means denominator have three zeroes or degree 3.

Only expression 1 has denominator with degree 3. The first expression is

[tex]\frac{x+2}{x^3-5x^2-24x}[/tex]

Equate denominator equal to 0.

[tex]x^3-5x^2-24x=0[/tex]

The roots of this equation are excluded values of the rational expression.

Taking out the common factor.

[tex]x(x^2-5x-24)=0[/tex]

[tex]x(x^2-8x+3x-24)=0[/tex]

[tex]x(x(x-8)+3(x-8))=0[/tex]

[tex]x(x+3)(x-8)=0[/tex]

Using zero product property, we get

[tex]x=0[/tex]

[tex]x+3=0\Rightarrow x=-3[/tex]

[tex]x-8=0\Rightarrow x=8[/tex]

The excluded values of first rational expression are –3, 0, and 8. Theretofore the correct option is 1.

Otras preguntas