chasechase
chasechase chasechase
  • 01-10-2018
  • Mathematics
contestada

The quotient of (x^4+5x^3-3x-15) and a polynomial is (x^3-3). What is the polynomial?

Respuesta :

JannetPalos
JannetPalos JannetPalos
  • 01-10-2018

Let f(x) be the required polynomial.

Then, [tex]\frac{x^{4}+5x^{3}-3x-15}{f(x)} =x^{3} -3[/tex]

Or, [tex]f(x) = \frac{x^{4}+15x^{3}-3x-15}{x^{3}-3 }[/tex]

Consider the numerator.

[tex]x^{4} +5x^{3} -3x-15 = x^{3}(x + 5)-3(x + 5)[/tex]

[tex]=(x^{3}- 3)(x+5)[/tex]

Therefore, [tex]\frac{x^{4}+5x^{3}-3x-15}{x^{3}-3 }[/tex]

= [tex]\frac{(x^{3}-3)(x+5) }{x^{3}-3 }[/tex]

= x + 5


Answer Link
milleraaron39
milleraaron39 milleraaron39
  • 11-01-2021

Answer:

x+5

Step-by-step explanation:

Edge 2020

Answer Link

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