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  • 24-03-2020
  • Mathematics
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Use the remainder theorem to find the remainder of 2x^4 + x^2 - 10x -1 divided by x +2.

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kudzordzifrancis
kudzordzifrancis kudzordzifrancis
  • 02-04-2020

Answer:

The remainder is 55

Step-by-step explanation:

Let

[tex]p(x)= 2 {x}^{4} + {x}^{2} - 10x - 1[/tex]

According to the remainder theorem, if p(x) is divided by x+a, the remainder is p (-a).

The given divisor is x+2, therefore the remainder is given by:

[tex]p( - 2)[/tex]

We substitute x=-2 to get:

[tex]p( - 2)= 2 {( - 2)}^{4} + {( - 2)}^{2} - 10( - 2) - 1[/tex]

We simplify to obtain:

[tex]p( - 2)= 2 \times 16 + 4 + 20- 1[/tex]

We multiply to get:

[tex]p( - 2)=3 2 + 4 + 20- 1 = 55[/tex]

Therefore the remainder is 55

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