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Tenth Grade (Grade 10) Polynomials and Rational Expressions Questions

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Grade 10 Polynomials and Rational Expressions
Match each factored expression with its corresponding expanded form.
__ [math]2(x-5)^2[/math] A. [math]3x^3-27x^2[/math]
__ [math]3x^2(x-9)[/math] B. [math]2x^2 + 2x-24[/math]
__ [math]2(x+4)(x-3)[/math] C. [math]x^3-x^2-5x+5[/math]
__ [math](x^2-5)(x-1)[/math] D. [math]2x^2 -20x+50[/math]
Grade 10 Polynomials and Rational Expressions CCSS: HSA-APR.D.7
Multiply. Simplify if possible. [math](2x^2)/5*25/x^3[/math]
  1. [math](2x^2 + 25)/(5x^3)[/math]
  2. [math](2x^5)/(125), \ \ x!=0[/math]
  3. [math]10/x[/math]
  4. [math]x/10, \ \ x!=0[/math]
Grade 10 Polynomials and Rational Expressions
Given: [math] (5x + 6)(8x - 4) [/math]

What is the product of the given?
  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 CCSS: HSA-SSE.A.2
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 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 10 Polynomials and Rational Expressions CCSS: HSA-APR.D.7
Divide. Simplify if possible. [math](x^2+x-90)/(x-3) -: (x-9)/(x^2-13x+30)[/math]
  1. [math]x-9, \ \ x!=3,9,10[/math]
  2. [math]((x+10)(x-9)^2)/((x-10)(x-3)^2), \ \ x!=9[/math]
  3. [math]((x-9)(x+10))/(x-10), \ \ x!=3,9[/math]
  4. [math]x^2-100, \ \ x!=3,9,10[/math]
Grade 10 Polynomials and Rational Expressions CCSS: HSA-APR.D.7
Divide. Simplify if possible. [math](x+3)/(7x) -: (x-3)/(21x)[/math]
  1. [math](3(x+3))/(x-3), \ \ x!=0[/math]
  2. [math]3, \ \ x!=0, 3[/math]
  3. [math]((x+3)(x-3))/(147x^2), \ \ x!=3[/math]
  4. [math](3(x-3))/(x+3), \ \ x!=0,3[/math]
Grade 10 Polynomials and Rational Expressions CCSS: HSA-APR.D.7
Add. Simplify the result if possible. [math]5/(15x)+6/(15x) [/math]
  1. [math]11/(15x)[/math]
  2. [math]1, \ \ x!=0[/math]
  3. [math](15x)/11, \ \ x!=0[/math]
  4. [math]11/(30x)[/math]
Grade 10 Polynomials and Rational Expressions
Write the expression [math](x + 5)(x + 2)[/math] as a polynomial in standard form.
  1. [math] x^2 + 3x + 10 [/math]
  2. [math] x^2 - 3x + 7 [/math]
  3. [math] x^2 +7x + 10 [/math]
  4. [math] x^2 +3x -3 [/math]
Grade 10 Polynomials and Rational Expressions CCSS: HSA-APR.D.7
Multiply. Simplify if possible. [math](x+7)/(x-2) * (x^2+5x-14)/(x-1)[/math]
  1. [math]x-1, \ \ x!=1,2[/math]
  2. [math]((x+7)^2)/(x-1), \ \ x!=2[/math]
  3. [math](x-1)/((x-2)^2), \ \ x!=1[/math]
  4. [math]1/(x-1), \ \ x!=2[/math]
Grade 10 Polynomials and Rational Expressions CCSS: HSA-APR.D.7
Divide. Simplify if possible. [math](x^2-12x+36)/(2x-12)-:(5x-30)/10[/math]
  1. [math]x-6, \ \ x!=6[/math]
  2. [math]1/(x-6)[/math]
  3. [math](x-6)^2/4, \ \ x!= 6[/math]
  4. [math]1, \ \ x!=6[/math]
Grade 10 Polynomials and Rational Expressions CCSS: HSA-APR.D.7
Subtract. Simplify if possible. [math](9x^2)/(x-1)-(9x)/(x-1)[/math]
  1. [math](9x(x+1))/(x+1), \ \ x!=1[/math]
  2. [math](9x)/(x-1)[/math]
  3. [math]0, \ \ x!=1[/math]
  4. [math]9x, \ \ x!=1[/math]
Grade 10 Polynomials and Rational Expressions
Identify the property used to begin the factoring of the given polynomial.

Given: [math] 7p^3r - 5t^3s - 21p^2r -10s^3t^3 [/math]

Step 1: [math] 7p^3r- 21p^2r - 5t^3s -10s^3t^3 [/math]
  1. Associative Property
  2. Commutative Property
  3. Distributive Property
  4. Substitution Property
Grade 10 Polynomials and Rational Expressions
Factor by grouping.
[math]15x^3-6x^2-25x+10[/math]
  1. [math](5x-5)(3x^2-2)[/math]
  2. [math](x-2)(15x^2-5)[/math]
  3. [math](15x-2)(x^2-5)[/math]
  4. [math](5x-2)(3x^2-5)[/math]
Grade 10 Polynomials and Rational Expressions
Simplify the expression.
[math](9x^3+2)+(2x^3-1)[/math]
  1. [math]11x^3+1[/math]
  2. [math]7x^3+1[/math]
  3. [math]9x^3-1[/math]
  4. [math]10x^3-1[/math]
Grade 10 Polynomials and Rational Expressions CCSS: HSA-APR.D.7
Divide. Simplify if possible. [math](x^2-25)/(x^2 + 4x + 4) -: (x^2-10x+25)/(x^2 + 7x+10)[/math]
  1. [math]((x-5)^3)/((x+2)^3), \ \ x!=-5,5[/math]
  2. [math](x+5)^2/((x+2)(x-5)), \ \ x!=-5[/math]
  3. [math](x-5)/(x+2), \ \ x!=-5,5[/math]
  4. [math](x+2)/(x-5), \ \ x!=-5,-2[/math]
Grade 10 Polynomials and Rational Expressions CCSS: HSA-APR.D.7
Multiply. Simplify if possible. [math](2x-2)/x * (8x^2)/(3x-3)[/math]
  1. [math]3/(16x), \ \ x!= 1[/math]
  2. [math](3(x+1)^2)/(4x^2), \ \ x!=1[/math]
  3. [math](16x)/3, \ \ x!= 0,1[/math]
  4. [math](16x-1)/(3x^2), \ \ x!=1[/math]
Grade 10 Polynomials and Rational Expressions CCSS: HSA-SSE.B.3, HSA-SSE.B.3a
Factor: [math]9y^2 - 25[/math]
  1. [math](3y + 5) (3y - 5)[/math]
  2. [math](9y + 5) (9y - 5)[/math]
  3. [math](9y - 25) (y + 1)[/math]
  4. [math](3y + 30) (3y - 5)[/math]
Grade 10 Polynomials and Rational Expressions
Name the polynomial by degree and the number of terms.
[math] 9x^3-10x^5+26[/math]
  1. Quintic Trinomial
  2. Quintic Monomial
  3. Quintic Binomial
  4. Quintic Polynomial
Grade 10 Polynomials and Rational Expressions
What type of polynomial has two terms?
  1. monomial
  2. binomial
  3. trinomial
  4. polynomial
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