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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. [math](x+2)(x-2)=x^2-4[/math]
  2. [math](30+2)(30-2)=900-4[/math]
  3. [math](2x+1)(2x-1)=4x^2-1[/math]
  4. [math](a+b)(a-b)=a^2-b^2[/math]
  5. [math](2a+3b)(2a-3b)=2a^2-3b^2[/math]
Grade 10 Polynomials and Rational Expressions CCSS: HSA-APR.C.4
Which one of the following is NOT true?
  1. [math](a+b)^2=a^2+2ab+b^2[/math]
  2. [math]a^2+4a+4=(a+2)^2[/math]
  3. [math]a^2-2ab+b^2=(a-b)^2[/math]
  4. [math]a^2-6ab-9b^2=(a-3b)^2[/math]
  5. [math](3a+2b)^2=9a^2+12ab+4b^2[/math]
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.C.4
Factor. [math]27x^3 + 64[/math]
  1. [math](3x-4)(9x^2 + 12x + 16) [/math]
  2. [math](3x + 4)(9x^2 - 12x + 16)[/math]
  3. [math](3x+4)(9x^2 + 12x + 16)[/math]
  4. [math]"Can't factor further"[/math]
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. [math]n^2 + n = 2n[/math]
  2. [math]n^2 + n = n/2[/math]
  3. [math]n^2 + n = n(n+1)[/math]
  4. [math]n^2 + n = n^2(1+n)[/math]
Grade 12 Polynomials and Rational Expressions CCSS: HSA-APR.C.4
[math](a+b)^2[/math]
Step 1: [math](a+b)(a+b)[/math]
Step 2: [math]a^2+ab+ab+b^2[/math]
Step 3: [math]a^2+ab^2+b^2[/math]
  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
[math](x^2 + y^2)^2[/math]
Step 1: [math](x^2+y^2)(x^2+y^2)[/math]
Step 2: [math]x^4+2x^2y^2+y^4[/math]
Step 3: [math](x^2+y^2)^2+(2xy)^2[/math]
  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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