Ok, so
We got the polynomial:
[tex]P(x)=x^4+2x^3-4x^2+4[/tex]
We are going to find P(-3) using the remainder theorem.
For this, we got that if P(-3), then we can write x+3 as a probable root of the polynomial.
We are going to write the coefficients of each term below, and use the theorem for x=-3.
As the remainder is -5, the value of P(-3) is -5.
The quotient will be:
The quotient is equal to the following function:
[tex]f(x)=x^3-x^2-x+3[/tex]
quotient: x^3-x^2-x+3
