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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 11 Polynomials and Rational Expressions CCSS: HSA-APR.D.6
Simplify the expression 7x2-63x+3.
  1. x+37, x≠-3
  2. 7x2-9x, x≠-3
  3. 7(x+3), x≠-3
  4. 7(x-3), x≠-3
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.D.6
Simplify.
x2-9x2+6x+9
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.D.6
Use synthetic division to divide the polynomials: x3+12x2+20x-96x-2.
  1. x2+14x+8+-4x-2
  2. x2+14x+48
  3. x3+8+-4x-2
  4. x2+8x+48
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.D.6
Simplify. x2y-x5y7+x8y4x2y
  1. 1-x3y6+x6y3,    x,y≠0
  2. x4y2-x7y8+x10y5,    x,y≠0
  3. x6y3-x3y6-1,    x,y≠0
  4. xy-x3y6+x6y3,    x,y≠0
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.D.6
Use synthetic division to divide the polynomials: 3m2+16m-12m+6.
  1. 3m-2
  2. m-2
  3. 3m-2+8m-2
  4. 3m+2
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.D.6
Simplify. x2-y2y2-49y-xy+7
  1. y-xy-7, x≠y,y≠-7
  2. -x+yy-7, x≠y,y≠-7
  3. -x-y-y-7, x≠y,y≠7
  4. -x-yy-7, x≠y,y≠-7
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.D.6
Use synthetic division to divide the polynomials: x3+64x+4.
  1. x2+16
  2. x2-16x+4
  3. x2-4x+16
  4. x2-4
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.D.6
Simplify the rational expression.

3x(x-3)(x-3)(x+3)
  1. x-3x,  x≠-3,3
  2. 3xx+3,  x≠3
  3. x+3x-3,  x≠-3
  4. 1x-3,  x≠-3
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.D.6
Use synthetic division to divide the polynomials: z3-8z-2.
  1. z2-2z+4
  2. z2+4z+4
  3. z2+2z+4
  4. z2+2z-4
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.D.6
Simplify the following.

yx-xyx+yxy
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.D.6
Use long division or synthetic division to divide the polynomials: (4x2-9)÷(2x+3).
  1. 2x+3
  2. 2x-3
  3. -2x+3
  4. -2x-3
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.D.6
Use long division or synthetic division to divide the polynomials: (x2-4)÷(x+4).
  1. x-4
  2. x+4+12x+4
  3. x-4+12x+4
  4. x+4
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.D.6
Divide x3-1 by x-2.
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.D.6
Use synthetic division to divide the polynomials: (8x3+6x2+7)÷(x+2).
  1. 8x2-10x+20+-33x+2
  2. 8x2-10x+20+33x+2
  3. -8x2+10x-20+-33x+2
  4. 8x2-10x-20--33x+2
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.D.6
What is the quotient of (x3-3x2+4x-6)and(x-2)?
  1. x2-x+2
  2. x2-x+3
  3. x2-x+2+2x-2
  4. x2-x+2-2x-2
Grade 12 Polynomials and Rational Expressions CCSS: HSA-APR.D.6
What is the remainder of 5x2+2x-8 divided by x-3?
  1. -8
  2. x-53
  3. 43
  4. 51
Grade 12 Polynomials and Rational Expressions CCSS: HSA-APR.D.6
What is the remainder of x2+6x-2 divided by x-5?
  1. -7
  2. x-53
  3. 53
  4. -2
Grade 12 Polynomials and Rational Expressions CCSS: HSA-APR.D.6
What is the remainder of 4x2+2x-5 divided by x-2?
  1. -2
  2. x-15
  3. 15
  4. x+15
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