Question

Use the remainder theorem to find P (1) for P(x) = 2x - 3x' + 3x -3.Specifically, give the quotient and the remainder for the associated division and the value of P (1).미미2Quotient = 0Х$2Remainder =0P(1) =

Answer 1

Using the remainder theorem, we must find P(1) for:

`P(x)=2x^4-3x^3+3x-3`

1) Because we want to evaluate P(x) for x = 1, we must compute

`(2x^4-3x^3+3x-3)/(x-1)`

2) Now we make the synthetic division by putting a 1 in the division box:

The remainder from the division is:

`R=-1`

The quotient of the division is:

`2x^3-x^2+2x+2`

3) From the synthetic division we get a remainder R = -1, applying the Remainder Theorem we get that:

`P(1)=R=-1`

Summary

The answers are:

1)

`Quotient=2x^3-x^2+2x+2`

2)

`Remainder=-1`

3)

`P(1)=-1`