Dividing and factorising polynomial expressions test questions

1

When $$3{x^3} + 2{x^2} - 7x + 5$$ is divided by $$x - 2$$, what is the remainder?

2

When $${x^4} + 2{x^3} - {x^2} + 5$$ is divided by $$x - 3$$, what is the remainder?

3

Find the remainder when dividing the polynomial $$f(x) = 4{x^3} - 2x + 7$$ by $$(x - 1)$$

4

If $${x^4} + 2{x^3} - k{x^2} + 2x - 3$$ divides exactly by $$x+3$$, what is the value of $$k$$?

5

When $$2{x^3} + {x^2} - 5x + 2$$ is divided by $$2x - 1$$, what are the other factors?

6

One root of the equation $$4{x^3} - 8{x^2} - x + 2 = 0$$ is $$\frac{1}{2}$$.

What are the other roots?