Respuesta :

Answer:

[tex](x+1)^2(x-3)[/tex]

Step-by-step explanation:

Use the rational root theorem

Hi There!!

It's a factor, So the answer yes.

Step-by-step explanation:

Because, Factor [tex]x^3 - x^2 - 5x - 3[/tex] using the rational roots test.

If a polynomial function has integer coefficients, then every rational zero will have the form  [tex]\frac{p}{q}[/tex]  where  p  is a factor of the constant and  q  is a factor of the leading.

Coefficient

[tex]p =[/tex] ±[tex]1,[/tex] ±[tex]3[/tex]

[tex]q = +1[/tex]

Find every combination of  [tex]+\frac{p}{q}[/tex] . These are the possible roots of the polynomial function.

Substitute [tex]-1[/tex]  and simplify the expression. In this case, the expression is equal to [tex]0[/tex] so [tex]-1[/tex] is a root of the polynomial.

Since [tex]-1[/tex] is a known root, divide the polynomial by [tex]x - 1[/tex] to find the quotient polynomial. This polynomial can then be used to find the remaining roots.

[tex]x^3 - x^2 - 5x - by[/tex] [tex]x + 1.[/tex]

--------------------------------

[tex]x + 1[/tex]

Divide [tex]x^3 - x^2 - 5x - 3[/tex] by [tex]x + 1[/tex].

[tex]x^2 - 2x - 3[/tex]

Write [tex]x^3 - x^2 - 5x - 3[/tex] as a set of factors.

[tex](x + 1) (x^2 -2x - 3)[/tex]

Factor [tex]x^2 - 2x - 3[/tex] using the AC method.

[tex](x + 1) (x- 3) ( x+ 1)[/tex]

Remove unnecessary parentheses.

[tex](x + 1) (x- 3) ( x+ 1)[/tex]

So, Your best answer is [tex](x + 1) (x- 3) ( x+ 1)[/tex]

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