Question

Use the REMAINDER THEOREM to explain whether or not (x-2) is a factor of F(x)=x^4-2x^3+3x^2-10x+3

Answer 1

`(P(x))/(R(x))|(D(x))/(Q(x))`


`\frac{x^4-2x^3+3x^2-10x+3}{}|\frac{x-2}{}`


`(x^4-2x^3+3x^2-10x+3)/(-x^4+2x^3)|(x-2)/(x^3)`


`(3x^2-10x+3)/(-3x^2+6x)|(x-2)/(x^3+3x)`


`(-4x+3)/(4x-8)|(x-2)/(x^3+3x-4)`


`\frac{-5}{}|(x-2)/(x^3+3x-4)`


`\boxed{\boxed(x^4-2x^3+3x^2-10x+3)/(-5)}`


`R(x)=-5`