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Practice — Algebra • Division of polynomials

Division of polynomials

Difficulty: ★☆☆

465

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

Your Answer:

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

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

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

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

Solution:

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

\(x+2\)

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

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

\(3x^2+5x\)

\(3x^2+6x\)

\(-x-2\)

\(0\)

\((x^3+5x^2+5x-2)\div(x+2)=x^2+3x-1\).

Division of polynomials

Difficulty: ★☆☆

466

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

Your Answer:

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

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

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

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

Solution:

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

\(x-3\)

\(x^3-8x^2+22x-21\)

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

\(-5x^2+22x\)

\(-5x^2+15x\)

\(7x-21\)

\(0\)

\((x^3-8x^2+22x-21)\div(x-3)=x^2-5x+7\).

Division of polynomials

Difficulty: ★☆☆

467

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

Your Answer:

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

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

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

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

Solution:

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

\(x-1\)

)

\(3x^3-7x^2+6x-2\)

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

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

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

\(2x-2\)

\(0\)

\((3x^3-7x^2+6x-2)\div(x-1)=3x^2-4x+2\).

Division of polynomials

Difficulty: ★★☆

468

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

Your Answer:

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

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

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

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

Solution:

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

\(2x+1\)

)

\(2x^3-3x^2+8x+5\)

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

\(-4x^2+8x\)

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

\(10x+5\)

\(0\)

\((2x^3-3x^2+8x+5)\div(2x+1)=x^2-2x+5\).

Division of polynomials

Difficulty: ★★☆

469

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

Your Answer:

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

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

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

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

Solution:

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

\(2-x\)

)

\(5x^3-13x^2+10x-8\)

\(5x^3-10x^2\)

\(-3x^2+10x\)

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

\(4x-8\)

\(0\)

\((5x^3-13x^2+10x-8)\div(2-x)=-5x^2+3x-4\).