Given:
[tex]p(x)=2x^4+x^2-10x-1[/tex] divided by [tex]x+2[/tex]
To find:
The remainder.
Solution:
[tex]p(x)=2x^4+x^2-10x-1[/tex] divided by [tex]x+2[/tex]
Remainder theorem:
If a polynomial p(x) is divide by x - a, then the remainder is p(a).
[tex]x+2=0[/tex]
Subtract 2 from both sides, we get
[tex]x=-2[/tex]
substitute x = -2 in p(x).
[tex]p(-2)=2(-2)^4+(-2)^2-10(-2)-1[/tex]
[tex]=2(16)+(4)+20-1[/tex]
[tex]=32+4+19[/tex]
[tex]=55[/tex]
The remainder is 55.
