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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
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
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
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
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 CCSS: HSA-APR.A.1
Simplify: [math]2x^3y^{-3}\cdot 2x^{-1}y^3[/math]
  1. 1
  2. [math]4x^5y^6[/math]
  3. [math]2x^2[/math]
  4. [math]4x^2[/math]
  5. None of the above.
Grade 10 Polynomials and Rational Expressions CCSS: HSA-APR.A.1
What is the difference [math](x^4 - 3x^2 + 4x + 7) - (x^4 - 6x^3 + 4x)?[/math]
  1. [math]3x^3 + 7[/math]
  2. [math]6x^3 - 3x^2 + 7[/math]
  3. [math]6x^3 - 3x^2 + 8x + 7[/math]
  4. [math]3x^3 + 8x + 7[/math]
Grade 10 Polynomials and Rational Expressions
Step 1 : [math] 7p^3r- 21p^2r - 5t^3s -10s^3t^3 [/math]

Step 2: [math] (7p^3r- 21p^2r) + ( - 5t^3s -10s^3t^3) [/math]

Which of the following is the GCF for one of the pairs of terms in step 2?
  1. There are no common factors.
  2. [math]p^3r[/math] is a factor of [math](7p^3r- 21p^2r)[/math].
  3. [math]-5s[/math] is a factor of [math]( - 5t^3s -10s^3t^3)[/math].
  4. [math]7p^2r[/math] is a factor of [math](7p^3r- 21p^2r)[/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
What type of polynomial has two terms?
  1. monomial
  2. binomial
  3. trinomial
  4. polynomial
Grade 10 Polynomials and Rational Expressions
Select the polynomial that is written in standard form.
  1. [math]3x^2+4x^5-7x[/math]
  2. [math]4x^5+3x^2-7x[/math]
  3. [math]-7x+4x^5+3x^2[/math]
  4. [math]7+4x^5-3x^4+2x^3[/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
[math]c/a+3/4 =[/math]
  1. [math](4c+3a)/(4a)[/math]
  2. [math](3c+4a)/(4a)[/math]
  3. [math]((c+a)4)/(4a)[/math]
Grade 10 Polynomials and Rational Expressions
Grade 10 Polynomials and Rational Expressions
Factor: [math]15x^6 - 6x^3 + 9x^2[/math]
  1. [math]5x^4 (3x^2 -2x + 6)[/math]
  2. [math]3x^2 (5x^4 -2x + 3)[/math]
  3. [math]3x^4 (5x^2 - 2x +3)[/math]
  4. [math]2x^4 (7x^2 - 3x + 2)[/math]
Grade 10 Polynomials and Rational Expressions
What type of polynomial has three terms?
  1. monomial
  2. binomial
  3. trinomial
  4. polynomial
Grade 10 Polynomials and Rational Expressions
Name the polynomial by degree and the number of terms.
[math]-8x+15[/math]
  1. Linear Monomial
  2. Linear Binomial
  3. Linear Trinomial
  4. Linear Polynomial
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