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Polynomials and Rational Expressions Questions - All Grades

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Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.A.1
What is the product [math](x + 5)(x^3 - 2x -3)?[/math]
  1. [math]x^4 + 5x^3 - 2x^2 - 7x -15[/math]
  2. [math]x^4 + 5x^3 - 2x^2 - 13x - 15[/math]
  3. [math]x^4 + 5x^3 - 2x^2 - 10x - 15[/math]
  4. [math]x^4 + 5x^3 - 2x^2 - 3x - 15[/math]
Grade 9 Polynomials and Rational Expressions
Combine like terms.
[math]4x^2 + 5z + 18x^2[/math]
  1. [math]14x^2 + 5z[/math]
  2. [math]22x^2 + 5z[/math]
  3. [math]22x^2 - 5z[/math]
  4. [math]-18x^2 - 5z[/math]
Grade 11 Polynomials and Rational Expressions
Given: [math] (5x + 6)(8x - 4) [/math]

The product of the given is:
  1. [math] 13x + 2 [/math]
  2. [math] 40x - 24 [/math]
  3. [math] 40x^2 + 24 [/math]
  4. [math] 40x^2 - 20x + 48x - 24 [/math]
Grade 10 Polynomials and Rational Expressions
Which of the following represents the simplified polynomial expression, given [math]3x^2y(3x^2y^2+7xy^3-4y^4)[/math] ?
  1. [math]9x^4y^6+21x^2y^3-12x^2y^4[/math]
  2. [math]6x^2y^2+10x^2y^3-7x^2y^4[/math]
  3. [math]9x^4y^3+21x^3y^4-12x^2y^5[/math]
  4. [math]6x^4y^3+10x^3y^4-7x^2y^5[/math]
Grade 9 Polynomials and Rational Expressions
Subtract: [math](4x^2 - 2x + 8) - ( x^2 + 3x - 2)[/math]
  1. [math]3x^2 + x + 6[/math]
  2. [math]3x^2 + x + 10[/math]
  3. [math]3x^2 - 5x + 6[/math]
  4. [math]3x^2 - 5x + 10[/math]
Grade 10 Polynomials and Rational Expressions
Factor the expression.
[math]x^4 - y^4[/math]
  1. [math](x - y)^4[/math]
  2. [math](x^2 + y^2)(x + y)(x - y)[/math]
  3. [math](x^2 + y^2)(x^2 - y^2)[/math]
  4. Can't be factored
Grade 9 Polynomials and Rational Expressions
Simplify the following polynomial by combining like terms. [math](3x^4 + 5x^3 - 7x^2) + (5x^5 - 3x^4 + 2x^2)[/math]
  1. [math]8x^4 + 8x^3 + 9x^2[/math]
  2. [math]5x^5 + 5x^3 + 9x^2[/math]
  3. [math]5x^5 + 5x^3 - 5x^2[/math]
  4. [math]5x^5 + 6x^4 + 5x^3 + 9x^2[/math]
Grade 9 Polynomials and Rational Expressions
Multiply:
[math](4x-1)(3x+2)[/math]
  1. [math]12x^2+3x-2[/math]
  2. [math]12x^2-5x+1[/math]
  3. [math]12x^2+11x+2[/math]
  4. [math]12x^2+5x-2[/math]
Grade 11 Polynomials and Rational Expressions
Simplify. [math](a - 1)/[(a)^2-1][/math]
  1. [math]1/a, \ a!=0[/math]
  2. [math]1/(a - 1), \ a!= -1[/math]
  3. [math]1/(1- a), \ a!=1 [/math]
  4. [math]1/(a + 1), \ a!=1[/math]
Grade 9 Polynomials and Rational Expressions
What is the simplest form of [math](3c^2 - 8c + 5) + (c^2 - 8c - 6)[/math]?
  1. [math]3c^2 - 1[/math]
  2. [math]4c^2 + 11[/math]
  3. [math]4c^2 - 16c - 1[/math]
  4. [math]2c^2 - 16c - 1[/math]
Grade 9 Polynomials and Rational Expressions
Find the greatest common factor of [math]6xyz + 12x^2y - 3yz^2[/math].
  1. [math]3xy[/math]
  2. [math]6yz[/math]
  3. [math]3y[/math]
  4. [math]2x^2y[/math]
Grade 9 Polynomials and Rational Expressions
Simplify: [math]2x^2+5+4x^2-3[/math]
  1. [math]2x^2-2[/math]
  2. [math]-2x^2+2[/math]
  3. [math]6x^2+2[/math]
  4. [math]6x^2+8[/math]
Grade 9 Polynomials and Rational Expressions
Simplify: [math]8x^3-4x+3x^3+6x^2-x[/math]
  1. [math]11x^3+6x^2-5x[/math]
  2. [math]11x^3+2x^2-x[/math]
  3. [math]5x^3+8x^2-3x[/math]
  4. [math]5x^3+6x^2+3x[/math]
Grade 9 Polynomials and Rational Expressions
Combine the polynomials.
[math](5x^3-2x^2+7x)+( -3x^3 + x^2 -5x)[/math]
  1. [math]2x^3+2x^2+2x[/math]
  2. [math]2x^3-x^2+2x[/math]
  3. [math]2x^3+3x^2+2x[/math]
  4. [math]2x^3+x^2+9x[/math]
Grade 9 Polynomials and Rational Expressions
Grade 9 Polynomials and Rational Expressions
Grade 11 Polynomials and Rational Expressions
Simplify the rational expression.

[math](3x(x-3))/((x-3)(x+3))[/math]
  1. [math](x-3)/x, \ \ x!=-3,3[/math]
  2. [math](3x)/(x+3), \ \ x!= 3[/math]
  3. [math](x+3)/(x-3), \ \ x!=-3[/math]
  4. [math]1/(x-3), \ \ x!= -3[/math]
Grade 9 Polynomials and Rational Expressions
Simplify the expression.
[math](2b^2 +8b - 10)+(-6b^2 +5 -3b)[/math]
  1. [math]-4b^2 +13b - 13[/math]
  2. [math]-4b^2 +5b - 15[/math]
  3. [math]-4b^2 +5b - 5[/math]
  4. [math]8b^2 +5b - 15[/math]
Grade 9 Polynomials and Rational Expressions
Simplify:
[math](xy^-6z^-3)/(x^-4y^-5z)[/math]
  1. [math](xz)/(x^4y^11z^3)[/math]
  2. [math](x^4y^4)/(y^6z^3)[/math]
  3. [math]x^5/(yz^4)[/math]
  4. [math](x^3y^5)/(y^3z^2)[/math]
Grade 9 Polynomials and Rational Expressions
Simplify: 5x + 12x
  1. 7x
  2. [math]7x^2[/math]
  3. 17x
  4. [math]17x^2[/math]
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