Using the remainder theorem, we must find P(1) for:
[tex]P(x)=2x^4-3x^3+3x-3[/tex]
1) Because we want to evaluate P(x) for x = 1, we must compute
[tex]\frac{2x^4-3x^3+3x-3}{x-1}[/tex]
2) Now we make the synthetic division by putting a 1 in the division box:
The remainder from the division is:
[tex]R=-1[/tex]
The quotient of the division is:
[tex]2x^3-x^2+2x+2[/tex]
3) From the synthetic division we get a remainder R = -1, applying the Remainder Theorem we get that:
[tex]P(1)=R=-1[/tex]
Summary
The answers are:
1)
[tex]Quotient=2x^3-x^2+2x+2[/tex]
2)
[tex]Remainder=-1[/tex]
3)
[tex]P(1)=-1[/tex]
