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Common Core Standard HSA-APR.D.6 Questions

Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.

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Grade 9 Polynomials and Rational Expressions CCSS: HSA-APR.D.6
What is [math](x^2 - 4xy + 4y^2)/(3xy - 6y^2)[/math] reduced to lowest terms?
  1. [math](x - 2y)/3[/math]
  2. [math](x - 2y) /(3y)[/math]
  3. [math](x + 2y)/3[/math]
  4. [math](x + 2y) / (3y)[/math]
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.D.6
Use synthetic division to divide the polynomials: [math](x^2+2x-63)/(x+9)[/math].
  1. [math]x-7[/math]
  2. [math]x+7[/math]
  3. [math]x^2-7[/math]
  4. [math]x^2+3x-54[/math]
Grade 10 Polynomials and Rational Expressions CCSS: HSA-APR.D.6
Simplify:

[math] (v^2 āˆ’5vāˆ’14 )/(v^2 +4v+4)[/math]
Grade 9 Polynomials and Rational Expressions CCSS: HSA-APR.D.6
Simplify [math](6x^2 + 21x + 9)/(4x^2 - 1)[/math] to lowest terms.
  1. [math]{3(x + 1)}/ (2x - 1)[/math]
  2. [math]{3(x + 3)}/(2x - 1)[/math]
  3. [math]{3(2x+3)}/{4(x - 1)}[/math]
  4. [math]{3(x + 3)}/(2x + 1)[/math]
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.D.6
Use synthetic division to divide the polynomials: [math](x^2-14x+45)/(x-5)[/math].
  1. [math]x+9[/math]
  2. [math]9-x[/math]
  3. [math]x+5[/math]
  4. [math]x-9[/math]
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.D.6
Solve using long division.

[math](x^3+7x^2-5x-6)/(x+2)[/math]
Grade 9 Polynomials and Rational Expressions CCSS: HSA-APR.D.6
What is [math](12a^3 - 20a^2)/(16a^2 +8a)[/math] reduced to lowest terms?
  1. [math]a/2[/math]
  2. [math](3a - 5)/(2a + 1)[/math]
  3. [math]-(2a)/(4+2a)[/math]
  4. [math](a(3a - 5))/(2(2a +1))[/math]
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.D.6
Use synthetic division to divide the polynomials: [math](y^2+14y+49)/(y+7)[/math].
  1. [math]y-7[/math]
  2. [math]y^2+7[/math]
  3. [math]y+7[/math]
  4. [math]y+(7)/(y+7)[/math]
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.D.6
When [math]2x^3 +3x^2 -2x+3[/math] is divided by [math]2x-1[/math], what is the remainder?
  1. [math]0[/math]
  2. [math]1/2[/math]
  3. [math]3[/math]
  4. [math]6[/math]
Grade 9 Polynomials and Rational Expressions CCSS: HSA-APR.D.6
Simplify: [math](5x^3)/(10x^7)[/math]
  1. [math]2x^4[/math]
  2. [math]1/(2x^4)[/math]
  3. [math]1/(5x^4)[/math]
  4. [math]x^4/5[/math]
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.D.6
Use synthetic division to divide the polynomials: [math](x^2-5x-24)/(x-8)[/math].
  1. [math]x^2+3[/math]
  2. [math]x+3[/math]
  3. [math]x-3[/math]
  4. [math]x+3+(8)/(x-8)[/math]
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.D.6
Simplify the expression [math](x-7)/(x^2-x-42)[/math].
  1. [math]1/(x+7), \ x!=-6[/math]
  2. [math]1/(x+6), \ x!= 7[/math]
  3. [math]x+7, \ x!= -6, 7[/math]
  4. [math]x+6, \ x!= -6, 7[/math]
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.D.6
Simplify:
[math](y^4 +y^2)/y^2[/math]
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.D.6
Use synthetic division to divide the polynomials: [math](x^2+7x+7)/(x+3)[/math].
  1. [math](x+4)/(x+3)[/math]
  2. [math]x+5[/math]
  3. [math]x+4+(5)/(x+3)[/math]
  4. [math]x+4+(-5)/(x+3)[/math]
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.D.6
Simplify the expression [math](7x^2-63)/(x+3)[/math].
  1. [math](x+3)/7, \ x!=-3[/math]
  2. [math](7x^2-9)/(x), \ x!=-3[/math]
  3. [math]7(x+3), \ x!=-3[/math]
  4. [math]7(x-3), \ x!=-3[/math]
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.D.6
Simplify.
[math](x^2-9)/(x^2+6x+9)[/math]
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.D.6
Use synthetic division to divide the polynomials: [math](x^3+12x^2+20x-96)/(x-2)[/math].
  1. [math]x^2+14x+8+(-4)/(x-2)[/math]
  2. [math]x^2+14x+48[/math]
  3. [math]x^3+8+(-4)/(x-2)[/math]
  4. [math]x^2+8x+48[/math]
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.D.6
Simplify. [math](x^2y-x^5y^7+x^8y^4)/(x^2y)[/math]
  1. [math]1-x^3y^6+x^6y^3, \ \ \ \ x,y!=0[/math]
  2. [math]x^4y^2-x^7y^8+x^10y^5, \ \ \ \ x,y!=0[/math]
  3. [math]x^6y^3-x^3y^6-1, \ \ \ \ x,y!=0[/math]
  4. [math]xy-x^3y^6+x^6y^3, \ \ \ \ x,y!=0[/math]
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.D.6
Use synthetic division to divide the polynomials: [math](3m^2+16m-12)/(m+6)[/math].
  1. [math]3m-2[/math]
  2. [math]m-2[/math]
  3. [math]3m-2+(8)/(m-2)[/math]
  4. [math]3m+2[/math]
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.D.6
Simplify. [math]((x^2-y^2)/(y^2-49))/((y-x)/(y+7))[/math]
  1. [math](y-x)/(y-7), \ x!=y, y!=-7[/math]
  2. [math](-x+y)/(y-7), \ x!=y, y!= -7[/math]
  3. [math](-x-y)/(-y-7), \ x!=y, y!=7[/math]
  4. [math](-x-y)/(y-7), \ x!=y, y!=-7[/math]
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