Singapore GCE O-Level · Additional Mathematics

Polynomials and the remainder theorem

23 practice questions, each with the answer and an explanation.

Practise Polynomials and the remainder theorem now

Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 23 questions

Find the remainder when $P (x) = x^{3} + 2 x^{2} - 3 x + 2$ is divided by $x - 5$ .
Find the remainder when $P (x) = x^{3} + 3 x^{2} - 3 x + 2$ is divided by $x + 4$ .
Find the remainder when $P (x) = x^{3} + x^{2} - 3 x + 2$ is divided by $x - 6$ .
Find the remainder when $P (x) = x^{3} + 4 x^{2} - 3 x + 2$ is divided by $x - 3$ .
Find the remainder when $P (x) = x^{3} - 2 x^{2} - 3 x + 2$ is divided by $x - 7$ .
Find the remainder when $P (x) = x^{3} + 5 x^{2} - 3 x + 2$ is divided by $x - 1$ .
The polynomial $x^{3} - 2 x^{2} + a x + 6$ has $x - 1$ as a factor. Find the value of $a$ .
The polynomial $x^{3} - 2 x^{2} + a x + 6$ has $x - 2$ as a factor. Find the value of $a$ .
The polynomial $x^{3} - 2 x^{2} + a x + 6$ has $x - 3$ as a factor. Find the value of $a$ .
The polynomial $x^{3} - 2 x^{2} + a x + 6$ has $x + 1$ as a factor. Find the value of $a$ .
The polynomial $x^{3} - 2 x^{2} + a x + 6$ has $x + 2$ as a factor. Find the value of $a$ .
Given that $x - 1$ is a factor of $x^{3} - 6 x^{2} + 11 x - 6$ , find the other two roots of $x^{3} - 6 x^{2} + 11 x - 6 = 0$ .
Given that $x - 1$ is a factor of $x^{3} - 2 x^{2} - 5 x + 6$ , find the other two roots of $x^{3} - 2 x^{2} - 5 x + 6 = 0$ .
Given that $x - - 1$ is a factor of $x^{3} - 5 x^{2} + 2 x + 8$ , find the other two roots of $x^{3} - 5 x^{2} + 2 x + 8 = 0$ .
Given that $x - 2$ is a factor of $x^{3} - 4 x^{2} + x + 6$ , find the other two roots of $x^{3} - 4 x^{2} + x + 6 = 0$ .
Given that $x - 1$ is a factor of $x^{3} - 3 x^{2} - 6 x + 8$ , find the other two roots of $x^{3} - 3 x^{2} - 6 x + 8 = 0$ .
Find the remainder when $x^{3} - 2 x^{2} + 4$ is divided by $x - 3$ .
Find the remainder when $2 x^{3} + x - 5$ is divided by $2 x - 1$ .
Given that $x + 2$ is a factor of $x^{3} + a x + 6$ , find the value of $a$ .
Factorise completely $x^{3} - 7 x + 6$ .
Solve the equation $x^{3} + 2 x^{2} - 5 x - 6 = 0$ .
When $x^{3} + a x^{2} + b x - 6$ is divided by $x - 1$ the remainder is $- 4$ , and $x - 2$ is a factor. Find the value of $a$ .
Find the remainder when $x^{4} + 1$ is divided by $x + 1$ .

Keep practising

Ready for the full Singapore GCE O-Level test?

Take a mock test Singapore GCE O-Level hub

Polynomials and the remainder theorem

Practise Polynomials and the remainder theorem now

All 23 questions

Keep practising

More Singapore GCE O-Level topics

Ready for the full Singapore GCE O-Level test?