Division of polynomials
Difficulty: ★☆☆Divide \(x^3+5x^2+5x-2\) by \(x+2\). Choose the correct simplified result.
Division of polynomials
Difficulty: ★☆☆Divide \(x^3-8x^2+22x-21\) by \(x-3\). Choose the correct simplified result.
Division of polynomials
Difficulty: ★☆☆Divide \(3x^3-7x^2+6x-2\) by \(x-1\). Choose the correct simplified result.
Division of polynomials
Difficulty: ★★☆Divide \(2x^3-3x^2+8x+5\) by \(2x+1\). Choose the correct simplified result.
Division of polynomials
Difficulty: ★★☆Divide \(5x^3-13x^2+10x-8\) by \(2-x\). Choose the correct simplified result.
Division of polynomials
Difficulty: ★★☆Divide \(6x^4+13x-19\) by \(1-x\). Choose the correct simplified result.
Quotient and remainder
Difficulty: ★★☆When \(x^3+2x^2+5x-4\) is divided by \(x+1\), which pair gives the quotient and the remainder?
Quotient and remainder
Difficulty: ★★☆When \(6x^3+7x^2-6\) is divided by \(x-2\), which pair gives the quotient and the remainder?
Quotient and remainder
Difficulty: ★★★When \(8x^3+x^2-2x+1\) is divided by \(2x-1\), which pair gives the quotient and the remainder?
Quotient and remainder
Difficulty: ★★★When \(2x^3-9x^2-9\) is divided by \(3-x\), which pair gives the quotient and the remainder?
Quotient and remainder
Difficulty: ★★★When \(x^3+5x^2-3x-1\) is divided by \(x^2+2x+1\), which pair gives the quotient and the remainder?
Quotient and remainder
Difficulty: ★★★When \(5x^4-2x^2-13x+8\) is divided by \(x^2+1\), which pair gives the quotient and the remainder?
Difference of cubes
Difficulty: ★★☆Choose the correct factorisation of \(x^3-y^3\).
Sum of cubes
Difficulty: ★★☆Choose the correct factorisation of \(x^3+y^3\).
Factor check
Difficulty: ★★☆Dividing \(2x^3+7x^2-43x+42\) by \(x-2\) gives which quotient?
Factorising a cubic
Difficulty: ★★★Solve \(2x^3+7x^2-43x+42=0\).
Give the roots in ascending order, separated by commas.
Factor check
Difficulty: ★★☆Dividing \(12x^3+16x^2-3x-4\) by \(2x+1\) gives which quotient?
Solving a cubic
Difficulty: ★★★Solve \(12x^3+16x^2-3x-4=0\).
Give the roots in ascending order, separated by commas.
Factor check
Difficulty: ★★☆Dividing \(x^3-x^2+2x+4\) by \(x+1\) gives which quotient?
Only real root
Difficulty: ★★☆Find the only real root of \(x^3-x^2+2x+4=0\).
Cubic with a known root
Difficulty: ★★★Given that \(x=5\) is a root of \(2x^3-5x^2-28x+15=0\), solve the equation.
Give the roots in ascending order, separated by commas.
Polynomial division by linear and quadratic factors: check 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
\(\displaystyle P(x)=\)\(x^{3} + 15 x^{2} - 52 x + 13\). Divide by \(x - 3\), where \(\displaystyle d=3\).
Find the \(\displaystyle x^{2}\) coefficient of the quotient.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Polynomial division by linear and quadratic factors: review variant 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
\(\displaystyle P(x)=\)\(2 x^{3} + 11 x^{2} - 73 x + 8\). Divide by \(x - 4\), where \(\displaystyle d=4\).
Find the \(\displaystyle x^{2}\) coefficient of the quotient.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Polynomial division by linear and quadratic factors: check 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
\(\displaystyle P(x)=\)\(2 x^{3} + 11 x^{2} - 73 x + 8\). Divide by \(x - 4\), where \(\displaystyle d=4\).
Find the x coefficient of the quotient.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Polynomial division by linear and quadratic factors: review variant 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
\(\displaystyle P(x)=\)\(3 x^{3} + 14 x^{2} - 36 x + 13\). Divide by \(x - 2\), where \(\displaystyle d=2\).
Find the x coefficient of the quotient.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Polynomial division by linear and quadratic factors: check 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
Divide \(\displaystyle P(x)=\)\(x^{4} + 18 x^{3} - 34 x^{2} + 53 x + 12\) by \(\displaystyle D(x)=\)\(x^{2} - 2 x + 2\). Write \(\displaystyle P=DQ+R\) with deg R<2.
Find the x coefficient of the remainder.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Polynomial division by linear and quadratic factors: review variant 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
Divide \(\displaystyle P(x)=\)\(2 x^{4} + 13 x^{3} - 69 x^{2} + 107 x + 30\) by \(\displaystyle D(x)=\)\(x^{2} - 4 x + 5\). Write \(\displaystyle P=DQ+R\) with deg R<2.
Find the x coefficient of the remainder.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Polynomial division by linear and quadratic factors: check 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
Divide \(\displaystyle P(x)=\)\(2 x^{4} + 13 x^{3} - 69 x^{2} + 107 x + 30\) by \(\displaystyle D(x)=\)\(x^{2} - 4 x + 5\). Write \(\displaystyle P=DQ+R\) with deg R<2.
Find the constant term of the remainder.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Polynomial division by linear and quadratic factors: review variant 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
Divide \(\displaystyle P(x)=\)\(3 x^{4} + 4 x^{3} - 101 x^{2} + 237 x + 12\) by \(\displaystyle D(x)=\)\(x^{2} - 6 x + 10\). Write \(\displaystyle P=DQ+R\) with deg R<2.
Find the constant term of the remainder.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.