Polynomial Long Division and Remainder Theorem

how to find the remainder of p(x) = $$x^3+1$$  by $$x+1$$  

what is the alternative method in factor theorem instead of (see pic) ?

Given $$f\left(x\right)=3x^3-x^2-8x+14$$ and $$x-2.$$ Use synthetic division to find the remainder for the polynomial division: $$f\left(x\right)\div g\left(x\right).$$

Given $$P\left(x\right)=x^3-3x^2-2x+4$$ , use the Remainder and Factor Theorems to determine which statement is true?

Use the Remainder and Factor Theorems to determine which of the following binomials are factors of $$P\left(x\right)=x^3-8x^2+5x+14$$ . Select all that apply.

Use the Remainder Theorem to find the remainder when $$f\left(x\right)=2x^3+3x^2-11x-6$$ is divided by x−3 $$x-3$$ .

Find the value of  $$k$$ for which  $$x+4$$ is a factor of  $$x^3+5x^2-kx+48$$ . 

Use the remainder theorem to determine  $$P\left(x\right)$$ .

$$P\left(x\right)=-2x^2-5x+7\$$ for $$x=-3.$$

(a)  

The Remainder Theorem states that when a polynomial f(x) is divided by (x-c), the remainder is: