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P(x)=2x^4-x^3+2x^2-kP(x)=2x
4
−x
3
+2x
2
−kP, left parenthesis, x, right parenthesis, equals, 2, x, start superscript, 4, end superscript, minus, x, cubed, plus, 2, x, squared, minus, k where kkk is an unknown integer.
P(x)P(x)P, left parenthesis, x, right parenthesis divided by (x+1)(x+1)left parenthesis, x, plus, 1, right parenthesis has a remainder of 222.
What is the value of kkk?

Respuesta :

kudzordzifrancis

Answer:

k=3

Step-by-step explanation:

The given polynomial is

[tex]p(x) = 2 {x}^{4} - {x}^{3} + 2 {x}^{2} - k[/tex]

This polynomial is divided by x+1 and the remainder is 2.

We want to find the value of k.

We can find k, using the remainder theorem.

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

So

[tex]p( - 1) = 2[/tex]

This implies that:

[tex]2 {( - 1)}^{4} - {( - 1)}^{3} + 2 {( - 1)}^{2} - k = 2[/tex]

We simplify to get:

[tex]2 + 1 + 2 - k = 2[/tex]

[tex]5 - k = 2[/tex]

[tex]k = 5 - 2 = 3[/tex]

The value of k is 3.

graciesmithhh

Answer:

k=4

Step-by-step explanation:

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