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Common Core Standard HSA-APR.A.1 Questions

Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

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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 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 9 Polynomials and Rational Expressions CCSS: HSA-APR.A.1
[math]3a(2a^2-4a+6)[/math]
  1. [math]3a^3-a^2+18a[/math]
  2. [math]6a^2-12a+18[/math]
  3. [math]5a^3-a^2+9a[/math]
  4. [math]6a^3-12a^2+18a[/math]
Grade 9 Polynomials and Rational Expressions CCSS: HSA-APR.A.1
[math](-4m-n)-(2m+3n)[/math]
  1. [math]-2m-4n[/math]
  2. [math]-6m-4n[/math]
  3. [math]-6m+2n[/math]
  4. [math]-8m-2n[/math]
Grade 9 Quadratic Equations and Expressions CCSS: HSA-REI.B.4, HSA-REI.B.4b
Solve for [math]x[/math].
[math]3x^2-4=8[/math]
  1. x = -1, 1
  2. x = 12
  3. x = 4
  4. x = -2, 2
  5. x = 3
Grade 11 Quadratic Equations and Expressions
What is the simplified form of [math](3x^3y^-4)^-2?[/math]
Exponent answers must have positive exponents in them.
  1. [math]y^8/(6x^-2)[/math]
  2. [math](9y^8)/(x^6)[/math]
  3. [math](y^8)/(9x^6)[/math]
  4. [math](y^8)/(9x^-6)[/math]
Grade 12 Polynomials and Rational Expressions CCSS: HSA-APR.A.1
[math]1/(x^2-5x)+x/(x-5)=[/math]
  1. [math](x^2+1)/(x(x-5))[/math]
  2. [math](x+1)/(x-5)[/math]
  3. [math](x-1)/(x-5)[/math]
Grade 9 Polynomials and Rational Expressions CCSS: HSA-APR.D.7
Multiply the rational expressions and simplify as much as possible.
[math](3x^2)/(4x^3)*(-2x)/6[/math]
  1. [math]-1/4[/math]
  2. [math]-x/4[/math]
  3. [math](6x)/24[/math]
  4. [math]x^3/x^2[/math]
Grade 11 Exponents
Simplify. Answer must only have positive exponents.

[math](x^-3 * y^-4 * y^2 *x^1) / (x^5 * y^2)[/math]
  1. [math](x^-2 * y^-2)/(x^5 * y^2)[/math]
  2. [math](y^2 * x)/(x^8 * y^6)[/math]
  3. [math]1 / (x^8 * y^6)[/math]
  4. [math]1 / (x^7 * y^4)[/math]
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.D.7
[math](x^2-64)/(x(x+8))*x/(x-8)[/math] =
  1. [math] 1 , \ \ x!=-8,0,8 [/math]
  2. [math](x^3-64x)/((x+8)(x-8)), \ \ x!= 0[/math]
  3. [math](x^2-8)/(x^2-64), \ \ x!= 0[/math]
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 9 Polynomials and Rational Expressions
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 9 Polynomials and Rational Expressions CCSS: HSA-APR.D.6, HSA-APR.D.7
Simplify. [math]((x+5)(2x-1))/(2x(x+1)^2)*(x(x+1))/(2x-1)[/math]
  1. [math]1/2[/math]
  2. [math]x+5[/math]
  3. [math]1/(2(x+1)[/math]
  4. [math](x+5)/(2(x+1)[/math]
  5. [math](x+5)/(2x)[/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 9 Polynomials and Rational Expressions CCSS: HSA-APR.D.7
To add [math](-7a^3)/(2b) + (2a^2)/(4b^2)[/math], what do you need to multiply the top and bottom of the first fraction by?
  1. [math]b[/math]
  2. [math]2b[/math]
  3. [math]a[/math]
  4. [math]-7a[/math]
Grade 9 Algebraic Expressions
Simplify the expression.
[math]9y ^2 - 2y - 3y^2 + 5y[/math]
  1. [math]12 y^2 + 3y[/math]
  2. [math]6y^2 + 3y^2[/math]
  3. [math]6 y^2 + 3y [/math]
  4. [math] 6y^2 + 7y[/math]
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.D.6
What is the quotient of [math](x^3 - 3x^2 + 4x - 6) and (x - 2)?[/math]
  1. [math]x^2 - x + 2[/math]
  2. [math]x^2 - x + 3[/math]
  3. [math]x^2 - x + 2 + (2)/(x - 2)[/math]
  4. [math]x^2 - x + 2 - (2)/(x - 2)[/math]
Grade 9 Polynomials and Rational Expressions
What is the least common denominator?
[math]1/(x+1)+4/((x+1)(x-1)[/math]
  1. [math](x+1)(x-1)[/math]
  2. [math](x+1)(x+1)[/math]
  3. [math](x-1)[/math]
  4. [math](x+1)[/math]
Grade 9 Polynomials and Rational Expressions CCSS: HSA-APR.A.1
[math](3x^2y^3+xy^2)(x^4y-2x^2y^2)[/math]
  1. [math]3x^4y^2-6x^4y^6+x^5y^2-2x^3y^4[/math]
  2. [math]3x^6y^4-6x^4y^5+x^5y^3-2x^3y^4[/math]
  3. [math]3x^6y^4-6x^4y^5+x^4y^4-2x^2y^2[/math]
  4. [math]3x^4y^6-6x^5y^4+x^3y^5-2x^4y^3[/math]
Grade 9 Polynomials and Rational Expressions CCSS: HSA-APR.A.1
[math](2x+3)(5x-8)[/math]
  1. [math]10x^2+x-24[/math]
  2. [math]10x^2-31x-24[/math]
  3. [math]10x^2-x-24[/math]
  4. [math]7x^2+10x-5[/math]
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