A polynomial is an algebraic expression involving many terms and can be factorised using long division or synthetic division.

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

\[3\]

\[17\]

\[23\]

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

\[47\]

\[131\]

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

\[2\]

\[9\]

\[6\]

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

\[- 2\]

\[3\frac{1}{4}\]

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

\(x + 2\) and \(x - 1\)

\(x - 2\) and \(x + 1\)

\(2x - 2\) and \(x - 2\)

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

What are the other roots?

\(\frac{1}{2}\) and \(- 2\)

\(- \frac{1}{2}\) and \(2\)

\(\frac{1}{2}\) and \(2\)