Respuesta :

absor201

Answer:

x+5

Step-by-step explanation:

Given:

Dividend= x4 + 5x3 – 3x – 15

Quotient=(x3-3)

As per the rule of division of polynomial:

Dividend = Divisor × Quotient + Remainder

Divisor= required polynomial p(x)

remainder=0

x4 + 5x3 – 3x – 15= p(x) *(x3-3) + 0

p(x)=x4 + 5x3 – 3x – 15/x3-3

By long division we get

p(x)= x+5 !

LudwigGR

Answer:

The polynomial is x+5.

Step-by-step explanation:

Here we need to recall the algorithm of the division for polynomials, which is very similar to the one for integers. Given polynomials P(x) and Q(x), there always exist polynomials S(x) and R(x) such that

P(x) = Q(x)S(x) + R(x)

where

  • R(x) is the remainder,
  • S(x) is the quotient,
  • Q(x) is the divisor,
  • P(x) is the dividend.

In this particular case,  

  • P(x) = x⁴+5x³-3x-15,
  • S(x) = x³-3
  • R(x) = 0
  • Q(x), is what we are looking for.

Then, x⁴+5x³-3x-15 = (x³-3)Q(x). In order to find Q(x) we must complete the division x⁴+5x³-3x-15/x³-3. This gives us that Q(x)=x+5.

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