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?