Algebraic divisionEdexcel International A Level Maths: Subtopic test

1. 1
   The polynomial $f(x)=x^3+2x^2-5x+1$ is divided by $(x-2)$.

   (a)

   Find the quotient.

   [1 mark]

   • A$x^2+4x+3$
   • B$x^2-5$
   • C$x^2+4x+7$
   • D$x^2+4x+3+\dfrac{7}{x-2}$

   (b)

   Find the remainder.

   [1 mark]

   • A$3$
   • B$-7$
   • C$7$
   • D$11$

   (c)

   Use the remainder theorem to check your remainder.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   Let $g(x)=6x^3+x^2-5x+7$.

   (a)

   $g(x)$ is divided by $(2x+1)$. Find the quotient.

   [1 mark]

   • A$3x^2+x-2$
   • B$3x^2-x-2$
   • C$6x^2-2x-4$
   • D$3x^2-x-2+\dfrac{9}{2x+1}$

   (b)

   $g(x)$ is divided by $(2x+1)$. Find the remainder.

   [1 mark]

   • A$7$
   • B$\dfrac{11}{2}$
   • C$3$
   • D$9$

   (c)

   Find the remainder when $g(x)$ is divided by $(x+2)$.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Let $f(x)=4x^3-8x^2+x+6$.

   (a)

   Find the quotient and the remainder when $f(x)$ is divided by $(2x-1)$.

   [3 marks]

   (b)

   The polynomial $p(x)=f(x)+kx$, where $k$ is a constant, leaves remainder $7$ when divided by $(2x+1)$. Find the value of $k$.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   The polynomial $f(x)=3x^3+ax^2-7x+b$, where $a$ and $b$ are constants, leaves remainder $12$ when divided by $(x-2)$ and remainder $-23$ when divided by $(3x+1)$.

   (a)

   Find the values of $a$ and $b$.

   [6 marks]

   (b)

   Given that $a=7$ and $b=-26$, find the quotient and the remainder when $f(x)$ is divided by $(x+1)$, and use the remainder theorem to check the remainder.

   [6 marks]

   Total for question 4: 12 marks

End of questions