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Use the factor theorem and synthetic division to decide whether the second polynomial is a factor of the first.
-x³+4x-15; x+3
Is x + 3 a factor of -x +4x-15?
Yes or no?

Respuesta :

ajeigbeibraheem

Yes, by using the factor theorem and synthetic division method, x + 3 is a factor of -x³ + 4x - 15.

What is the factor theorem?

According to the factor theorem, a given polynomial of f(x) has a factor if and only if f=0.

From the given information:

  • The factor of -x³ + 4x - 15 is -(x+3)(x² - 3x + 5) = 0

Using the synthetic division method:

[tex]\mathbf{= \dfrac{-x^3+4x - 5}{x+3} }[/tex]

[tex]\mathbf{\implies \dfrac{-(x+3) (x^2-3x + 5)}{x+3} }[/tex]

Cancel out the common factors, we have:

[tex]\mathbf{\implies - (x^2-3x + 5)}[/tex]

Learn more about factor theorem and synthetic division of polynomials here:

https://brainly.com/question/24380382

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