Polynomial Division by Quadratic Divisor - Polynomial Division & Manipulation

CAIE P2 2010 June Q4

6 marks Moderate -0.8

4 The polynomial $x ^ { 3 } + 3 x ^ { 2 } + 4 x + 2$ is denoted by $\mathrm { f } ( x )$.

Find the quotient and remainder when $\mathrm { f } ( x )$ is divided by $x ^ { 2 } + x - 1$.
Use the factor theorem to show that $( x + 1 )$ is a factor of $\mathrm { f } ( x )$.

CAIE P2 2005 November Q2

6 marks Moderate -0.3

2 The polynomial $x ^ { 3 } + 2 x ^ { 2 } + 2 x + 3$ is denoted by $\mathrm { p } ( x )$.

Find the remainder when $\mathrm { p } ( x )$ is divided by $x - 1$.
Find the quotient and remainder when $\mathrm { p } ( x )$ is divided by $x ^ { 2 } + x - 1$.

CAIE P2 2019 November Q1

3 marks Moderate -0.5

1 The polynomial $\mathrm { f } ( x )$ is defined by $$f ( x ) = x ^ { 4 } - 3 x ^ { 3 } + 5 x ^ { 2 } - 6 x + 11$$ Find the quotient and remainder when $\mathrm { f } ( x )$ is divided by $\left( x ^ { 2 } + 2 \right)$.

CAIE P3 2020 June Q1

3 marks Moderate -0.5

1 Find the quotient and remainder when $6 x ^ { 4 } + x ^ { 3 } - x ^ { 2 } + 5 x - 6$ is divided by $2 x ^ { 2 } - x + 1$.

CAIE P3 2023 June Q2

3 marks Moderate -0.5

2 Find the quotient and remainder when $2 x ^ { 4 } - 27$ is divided by $x ^ { 2 } + x + 3$.

CAIE P3 2024 March Q1

3 marks Moderate -0.5

1 Find the quotient and remainder when $x ^ { 4 } - 3 x ^ { 3 } + 9 x ^ { 2 } - 12 x + 27$ is divided by $x ^ { 2 } + 5$.

CAIE P3 2021 November Q1

3 marks Moderate -0.5

1 Find the quotient and remainder when $2 x ^ { 4 } + 1$ is divided by $x ^ { 2 } - x + 2$.

OCR C4 Specimen Q1

4 marks Moderate -0.8

1 Find the quotient and remainder when $x ^ { 4 } + 1$ is divided by $x ^ { 2 } + 1$.

OCR C4 2010 January Q1

4 marks Moderate -0.3

1 Find the quotient and the remainder when $x ^ { 4 } + 11 x ^ { 3 } + 28 x ^ { 2 } + 3 x + 1$ is divided by $x ^ { 2 } + 5 x + 2$.

OCR C4 2009 June Q1

4 marks Moderate -0.3

1 Find the quotient and the remainder when $3 x ^ { 4 } - x ^ { 3 } - 3 x ^ { 2 } - 14 x - 8$ is divided by $x ^ { 2 } + x + 2$.

OCR C4 2016 June Q1

3 marks Moderate -0.5

1 Find the quotient and the remainder when $4 x ^ { 3 } + 8 x ^ { 2 } - 5 x + 12$ is divided by $2 x ^ { 2 } + 1$.

CAIE P3 2017 November Q1

3 marks Moderate -0.8

Find the quotient and remainder when $x^4$ is divided by $x^2 + 2x - 1$. [3]

OCR C4 2005 June Q1

4 marks Moderate -0.8

Find the quotient and the remainder when $x^4 + 3x^3 + 5x^2 + 4x - 1$ is divided by $x^2 + x + 1$. [4]

OCR C4 Q2

4 marks Moderate -0.8

Find the quotient and remainder when $(x^4 + x^3 - 5x^2 - 9)$ is divided by $(x^2 + x - 6)$. [4]