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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 9 Polynomials and Rational Expressions CCSS: HSA-APR.A.1
Multiply. [math]5y(9y^2 + 2y - 6)[/math]
Grade 9 Polynomials and Rational Expressions CCSS: HSA-APR.A.1
[math]3(y - 2y^2) + 4(7 - 5y) + 8(y^2 - 7)[/math]
Grade 9 Polynomials and Rational Expressions CCSS: HSA-APR.A.1
[math](12c + 8d) - (7c - 5d)[/math]
  1. [math]19c - 3d[/math]
  2. [math]19c + 13d[/math]
  3. [math]5c - 3d[/math]
  4. [math]5c + 13d[/math]
Grade 9 Polynomials and Rational Expressions CCSS: HSA-APR.A.1
Multiply.

[math](5-3x)(9-6x-8x^2)[/math]
Grade 9 Polynomials and Rational Expressions CCSS: HSA-APR.A.1
[math]-a^2[/math] is classified as which of the following?
(select all that apply)
  1. Monomial
  2. Binomial
  3. Trinomial
  4. Polynomial
  5. None of the above
Grade 9 Polynomials and Rational Expressions CCSS: HSA-APR.A.1
Subtract.
[math](3a^3 -5a^2 +11) - (6a^3 - a - 2)[/math]
  1. [math]3a^3 - 5a^2 - a +9[/math]
  2. [math]-3a^3 - 4a^2 + 13[/math]
  3. [math]9a^3 - 5a^2 - a + 9[/math]
  4. [math]-3a^3 - 5a^2 + a + 13[/math]
Grade 9 Polynomials and Rational Expressions CCSS: HSA-APR.A.1
[math]2(z - z^2 + z^3) + 3(z - 2) + 9(-z^2 + 5)[/math]
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.A.1
Tommy is building a rectangular garden. His dimensions are [math]5x[/math] and [math]5x-4[/math]. Find the area of the rectangular garden he is building in terms of [math]x[/math]. (area = lw)
  1. [math]25x^2-20x[/math]
  2. [math]25x^2-4[/math]
  3. [math]25x^2 +5x - 4[/math]
  4. [math]25x - 20[/math]
Grade 9 Polynomials and Rational Expressions CCSS: HSA-APR.A.1
Multiply:
[math](4x-1)(3x+2)[/math]
  1. [math]12x^2+3x-2[/math]
  2. [math]12x^2-5x+1[/math]
  3. [math]12x^2+11x+2[/math]
  4. [math]12x^2+5x-2[/math]
Grade 9 Polynomials and Rational Expressions CCSS: HSA-APR.A.1
[math]5[/math] is classified as which of the following?
(select all that apply)
  1. Monomial
  2. Binomial
  3. Trinomial
  4. Polynomial
  5. None of the above
Grade 9 Polynomials and Rational Expressions CCSS: HSA-APR.A.1
Subtract the polynomials.
[math](-3z^2 + 9z -4) - (4z^2 -5 + z)[/math]
  1. [math]-7z^2 + 8z +1[/math]
  2. [math]-z^2 + 8z - 9[/math]
  3. [math]z^2 + 10z -9[/math]
  4. [math]7z^2 +4z -3[/math]
Grade 9 Polynomials and Rational Expressions CCSS: HSA-APR.A.1
Subtract and write the resulting polynomial in descending order of degree.

[math](10y+13)-(-6y+9)[/math]
  1. [math]16y+22[/math]
  2. [math]20y[/math]
  3. [math]-16y-4[/math]
  4. [math]16y+4[/math]
Grade 10 Polynomials and Rational Expressions CCSS: HSA-APR.A.1
[math]x(8x - 5y) - x(x - 6y) - 3x(3 + 3y)[/math]
  1. [math]9x^2 +15xy -14x[/math]
  2. [math]7x^2 - 8xy - 9x[/math]
  3. [math]9x^2 +xy - 18x[/math]
  4. [math]7x^2 + 8xy - 9x[/math]
Grade 9 Polynomials and Rational Expressions CCSS: HSA-APR.A.1
[math]x+5[/math] is described as which of the following?
(select all that apply)
  1. Monomial
  2. Binomial
  3. Trinomial
  4. Polynomial
  5. None of the above
Grade 9 Polynomials and Rational Expressions CCSS: HSA-APR.A.1
Subtract the polynomials.
[math](6x^3 - 4x^2y + 9xy^2 - 2y^3) - (xy^2 - 3x^2y + 4x^3 - 7y^3)[/math]
  1. [math]5x^3 - x^2y + 5xy^2 + 5y^3[/math]
  2. [math]2x^3 - x^2y + 8xy^2 +5y^3[/math]
  3. [math]2x^3 - 7x^2y + 8xy^2 - 9y^3[/math]
  4. [math]5x^3 -5x^2y + 12xy^2 - 9y^3[/math]
Grade 9 Polynomials and Rational Expressions CCSS: HSA-APR.A.1
[math](w^7-w^2+w) - (w^6+w^3-w)[/math]
Grade 9 Polynomials and Rational Expressions CCSS: HSA-APR.A.1
[math](2x^2 - 5x - 7) + (7x^2 + 3)[/math]
  1. [math]2x^2 + 2x - 4[/math]
  2. [math]9x^2 - 5x - 4[/math]
  3. [math]9x^2 - 2x - 7[/math]
  4. [math]9x^4 - 5x - 4[/math]
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