Practice Questions

Division of polynomials

Difficulty: ★☆☆

465

Divide \(x^3+5x^2+5x-2\) by \(x+2\). Choose the correct simplified result.

Your Answer:

\(x^2+3x-1\)

\(x^2+3x+1\)

\(x^2-3x-1\)

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

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Division of polynomials

Difficulty: ★☆☆

466

Divide \(x^3-8x^2+22x-21\) by \(x-3\). Choose the correct simplified result.

Your Answer:

\(x^2-5x+7\)

\(x^2+5x-7\)

\(x^2-5x-7\)

\(x^2-3x+7\)

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Division of polynomials

Difficulty: ★☆☆

467

Divide \(3x^3-7x^2+6x-2\) by \(x-1\). Choose the correct simplified result.

Your Answer:

\(3x^2-4x+2\)

\(3x^2+4x+2\)

\(3x^2-4x-2\)

\(x^2-4x+2\)

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Division of polynomials

Difficulty: ★★☆

468

Divide \(2x^3-3x^2+8x+5\) by \(2x+1\). Choose the correct simplified result.

Your Answer:

\(x^2-2x+5\)

\(x^2+2x+5\)

\(2x^2-2x+5\)

\(x^2-2x-5\)

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Division of polynomials

Difficulty: ★★☆

469

Divide \(5x^3-13x^2+10x-8\) by \(2-x\). Choose the correct simplified result.

Your Answer:

\(-5x^2+3x-4\)

\(5x^2+3x-4\)

\(-5x^2-3x-4\)

\(-5x^2+3x+4\)

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Division of polynomials

Difficulty: ★★☆

470

Divide \(6x^4+13x-19\) by \(1-x\). Choose the correct simplified result.

Your Answer:

\(-6x^3-6x^2-6x-19\)

\(6x^3+6x^2+6x+19\)

\(-6x^3-6x^2-19\)

\(-6x^3+6x^2-6x-19\)

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Quotient and remainder

Difficulty: ★★☆

471

When \(x^3+2x^2+5x-4\) is divided by \(x+1\), which pair gives the quotient and the remainder?

Your Answer:

Quotient \(=x^2+x+4\), remainder \(=-8\)

Quotient \(=x^2+x-4\), remainder \(=8\)

Quotient \(=x^2-x+4\), remainder \(=-8\)

Quotient \(=x^2+x+4\), remainder \(=8\)

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Quotient and remainder

Difficulty: ★★☆

472

When \(6x^3+7x^2-6\) is divided by \(x-2\), which pair gives the quotient and the remainder?

Your Answer:

Quotient \(=6x^2+19x+38\), remainder \(=70\)

Quotient \(=6x^2+19x-38\), remainder \(=70\)

Quotient \(=6x^2-19x+38\), remainder \(=70\)

Quotient \(=6x^2+19x+38\), remainder \(=-70\)

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Quotient and remainder

Difficulty: ★★★

473

When \(8x^3+x^2-2x+1\) is divided by \(2x-1\), which pair gives the quotient and the remainder?

Your Answer:

Quotient \(=4x^2+\tfrac52x+\tfrac14\), remainder \(=\tfrac54\)

Quotient \(=4x^2+\tfrac52x-\tfrac14\), remainder \(=\tfrac54\)

Quotient \(=4x^2-\tfrac52x+\tfrac14\), remainder \(=\tfrac54\)

Quotient \(=4x^2+\tfrac52x+\tfrac14\), remainder \(=-\tfrac54\)

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Quotient and remainder

Difficulty: ★★★

474

When \(2x^3-9x^2-9\) is divided by \(3-x\), which pair gives the quotient and the remainder?

Your Answer:

Quotient \(=-2x^2+3x+9\), remainder \(=-36\)

Quotient \(=2x^2-3x-9\), remainder \(=-36\)

Quotient \(=-2x^2+3x+9\), remainder \(=36\)

Quotient \(=2x^2+3x+9\), remainder \(=-36\)

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Quotient and remainder

Difficulty: ★★★

475

When \(x^3+5x^2-3x-1\) is divided by \(x^2+2x+1\), which pair gives the quotient and the remainder?

Your Answer:

Quotient \(=x+3\), remainder \(=-10x-4\)

Quotient \(=x-3\), remainder \(=-10x-4\)

Quotient \(=x+3\), remainder \(=10x-4\)

Quotient \(=x+1\), remainder \(=-10x-4\)

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Quotient and remainder

Difficulty: ★★★

476

When \(5x^4-2x^2-13x+8\) is divided by \(x^2+1\), which pair gives the quotient and the remainder?

Your Answer:

Quotient \(=5x^2-7\), remainder \(=-13x+15\)

Quotient \(=5x^2+7\), remainder \(=-13x+15\)

Quotient \(=5x^2-7\), remainder \(=13x+15\)

Quotient \(=5x^2-7\), remainder \(=-13x-15\)

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Difference of cubes

Difficulty: ★★☆

477

Choose the correct factorisation of \(x^3-y^3\).

Your Answer:

\((x-y)(x^2+xy+y^2)\)

\((x-y)(x^2-xy+y^2)\)

\((x+y)(x^2+xy+y^2)\)

\((x-y)(x^2+xy-y^2)\)

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Sum of cubes

Difficulty: ★★☆

478

Choose the correct factorisation of \(x^3+y^3\).

Your Answer:

\((x+y)(x^2-xy+y^2)\)

\((x+y)(x^2+xy+y^2)\)

\((x-y)(x^2-xy+y^2)\)

\((x+y)(x^2-xy-y^2)\)

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Factor check

Difficulty: ★★☆

479

Dividing \(2x^3+7x^2-43x+42\) by \(x-2\) gives which quotient?

Your Answer:

\(2x^2+11x-21\)

\(2x^2-11x-21\)

\(2x^2+11x+21\)

\(x^2+11x-21\)

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Factorising a cubic

Difficulty: ★★★

480

Solve \(2x^3+7x^2-43x+42=0\).

Give the roots in ascending order, separated by commas.

Your Answer:

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Factor check

Difficulty: ★★☆

481

Dividing \(12x^3+16x^2-3x-4\) by \(2x+1\) gives which quotient?

Your Answer:

\(6x^2+5x-4\)

\(6x^2-5x-4\)

\(6x^2+5x+4\)

\(3x^2+5x-4\)

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Solving a cubic

Difficulty: ★★★

482

Solve \(12x^3+16x^2-3x-4=0\).

Give the roots in ascending order, separated by commas.

Your Answer:

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Factor check

Difficulty: ★★☆

483

Dividing \(x^3-x^2+2x+4\) by \(x+1\) gives which quotient?

Your Answer:

\(x^2-2x+4\)

\(x^2+2x+4\)

\(x^2-2x-4\)

\(x^2+2x-4\)

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Only real root

Difficulty: ★★☆

484

Find the only real root of \(x^3-x^2+2x+4=0\).

Your Answer:

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Cubic with a known root

Difficulty: ★★★

485

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.

Your Answer:

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Practice — Algebra • Division of polynomials

Division of polynomials

Solution:

Division of polynomials

Solution:

Division of polynomials

Solution:

Division of polynomials

Solution:

Division of polynomials

Solution:

Division of polynomials

Solution:

Quotient and remainder

Solution:

Quotient and remainder

Solution:

Quotient and remainder

Solution:

Quotient and remainder

Solution:

Quotient and remainder

Solution:

Quotient and remainder

Solution:

Difference of cubes

Solution:

Sum of cubes

Solution:

Factor check

Solution:

Factorising a cubic

Solution:

Factor check

Solution:

Solving a cubic

Solution:

Factor check

Solution:

Only real root

Solution:

Cubic with a known root

Solution: