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