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Eleventh Grade (Grade 11) Polynomials and Rational Expressions Questions

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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 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 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 11 Polynomials and Rational Expressions CCSS: HSA-APR.A.1
Find the greatest common factor of the terms in the polynomial.

[math]9x^4 + 12x^3 +6x[/math]
  1. [math]2x^2[/math]
  2. [math]3x[/math]
  3. [math]6x^3[/math]
  4. [math]9x^4[/math]
Grade 11 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 11 Polynomials and Rational Expressions
Use the GCF of the terms to factor the polynomial.

Given: [math] 23x^4 + 46x^3 [/math]
  1. [math] x^3(23x+46) [/math]
  2. [math] 23x^3(x+2) [/math]
  3. [math] 23x^4(x+2) [/math]
  4. [math] 23x(x^3+2x^2) [/math]
Grade 11 Polynomials and Rational Expressions
Write the given polynomial in standard form.

Given: [math] 4g–g^3 +3g^2 –2 [/math]
  1. [math] –2+4g+3g^2–g^3 [/math]
  2. [math] 3g^3 –g^2 +4g–2 [/math]
  3. [math] g^3–3g^2+4g–2 [/math]
  4. [math] –g^3 +3g^2 +4g–2 [/math]
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.A.1
Which polynomial has the factorization [math](x - 10)(x^2 + 10x + 100)?[/math]
  1. [math]x^3 - 1000[/math]
  2. [math]x^3 - 100[/math]
  3. [math]x^3 + 100[/math]
  4. [math]x^3 + 1000[/math]
Grade 11 Polynomials and Rational Expressions
Find the Greatest Common Factor (GCF) of the terms of the given polynomial.

Given: [math] 8x^6 + 32x^3 [/math]
  1. [math] x^3 [/math]
  2. [math] 8x^3 [/math]
  3. [math] 4x^3 [/math]
  4. [math] 8x^6 [/math]
Grade 11 Polynomials and Rational Expressions
What are the coefficients of the given mathematical expression: [math] 7p^3r - 5t^3s -21p^2r - 10s^3t^3 [/math]
  1. [math] 3,1; 3,1; 2,1; 3,3 [/math]
  2. [math] 7, -5,- 21, -10 [/math]
  3. [math] 3, 3, 2, 3, 3 [/math]
  4. [math] -29p^5r^2s^4t^6 [/math]
Grade 11 Polynomials and Rational Expressions
Determine the best statement that describes the following:

[math] 40x^2 - 20x + 48x - 24 [/math]
  1. Is an expression that can be simplified to 3 terms. [math] 40x^2 + 28x - 24 [/math]
  2. Is an equation can be solved for the value of x. [math] x =6//17 [/math]
  3. Is an expression that can be simplified to 2 terms. [math] 68x -24 [/math]
  4. Is an expression that can be simplified to a term. [math] 44x [/math]
Grade 11 Polynomials and Rational Expressions
Grade 11 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 11 Polynomials and Rational Expressions
Which two properties are used to simplify the expression below?

(12p² + 15p + 3) - (2p² + 17p - 2)
  1. Associative and Distributive Property
  2. Commutative and Distributive Property
  3. Substitution and Distributive Property
  4. Substitution and Commutative Property
Grade 11 Polynomials and Rational Expressions
Find the values that make the rational expression undefined:

[math](x^2+3)/(x(x+5)[/math]
  1. [math]x=0[/math] or [math]-5[/math]
  2. [math]x=0[/math] or [math]7[/math]
  3. [math]x=0[/math] or [math]5[/math]
  4. [math]x=2[/math] or [math]4[/math]
Grade 11 Polynomials and Rational Expressions
Simplify the rational expression:

[math](2y)/(8y^2)[/math]
  1. [math]y/6[/math]
  2. [math](2y)/3[/math]
  3. [math]1/(4y)[/math]
  4. [math]2/(5y)[/math]
Grade 11 Polynomials and Rational Expressions
Find the value that makes the rational expression undefined:

[math]8/(y+6)[/math]
  1. [math]y= -4[/math]
  2. [math]y=0[/math]
  3. [math]y=3[/math]
  4. [math]y=-6[/math]
Grade 11 Polynomials and Rational Expressions
Evaluate the expresson:

[math](y+1)/(2y^2-3)[/math] when [math]y[/math] is [math]-2[/math]
  1. [math]-1[/math]
  2. [math]1/2[/math]
  3. [math]-1/5[/math]
  4. [math]10/19[/math]
Grade 11 Polynomials and Rational Expressions
Given: (5x + 6)(8x - 4).

The given is best described as:
  1. the multiplication of four monomials
  2. the multiplication of two binomials
  3. the multiplication of two monomials
  4. a monomial
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