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Common Core Standard HSA-APR.C.4 Questions

Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x2 + y2)2 = (x2 – y2)2 + (2xy)2 can be used to generate Pythagorean triples.

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Grade 10 Polynomials and Rational Expressions CCSS: HSA-APR.C.4
Which one of the following is NOT true?
  1. (a+b)2=a2+2ab+b2
  2. a2+4a+4=(a+2)2
  3. a2-2ab+b2=(a-b)2
  4. a2-6ab-9b2=(a-3b)2
  5. (3a+2b)2=9a2+12ab+4b2
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.C.4
Factor. 27x3+64
  1. (3x-4)(9x2+12x+16)
  2. (3x+4)(9x2-12x+16)
  3. (3x+4)(9x2+12x+16)
  4. Can't factor further
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.C.4
Which of the following is a correct polynomial identity that illustrates the statement "the sum of any integer and its value squared is an even number"?
  1. n2+n=2n
  2. n2+n=n2
  3. n2+n=n(n+1)
  4. n2+n=n2(1+n)
Grade 10 Polynomials and Rational Expressions CCSS: HSA-APR.C.4
Which one of the following is NOT true?
  1. (x+2)(x-2)=x2-4
  2. (30+2)(30-2)=900-4
  3. (2x+1)(2x-1)=4x2-1
  4. (a+b)(a-b)=a2-b2
  5. (2a+3b)(2a-3b)=2a2-3b2
Grade 12 Polynomials and Rational Expressions CCSS: HSA-APR.C.4
(a+b)2
Step 1: (a+b)(a+b)
Step 2: a2+ab+ab+b2
Step 3: a2+ab2+b2
  1. The proof is correct.
  2. Step 1 has an error.
  3. Step 2 has an error.
  4. Step 3 has an error.
Grade 12 Polynomials and Rational Expressions CCSS: HSA-APR.C.4
(x2+y2)2
Step 1: (x2+y2)(x2+y2)
Step 2: x4+2x2y2+y4
Step 3: (x2+y2)2+(2xy)2
  1. The proof is correct.
  2. Step 1 has an error.
  3. Step 2 has an error.
  4. Step 3 has an error.

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