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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 11 Polynomials and Rational Expressions CCSS: HSA-APR.A.1
What is the product $(x + 5)(x^3 - 2x -3)?$
1. $x^4 + 5x^3 - 2x^2 - 7x -15$
2. $x^4 + 5x^3 - 2x^2 - 13x - 15$
3. $x^4 + 5x^3 - 2x^2 - 10x - 15$
4. $x^4 + 5x^3 - 2x^2 - 3x - 15$
Grade 10 Polynomials and Rational Expressions CCSS: HSA-APR.A.1
Simplify: $2x^3y^{-3}\cdot 2x^{-1}y^3$
1. 1
2. $4x^5y^6$
3. $2x^2$
4. $4x^2$
5. None of the above.
Grade 9 Polynomials and Rational Expressions CCSS: HSA-APR.A.1
$3a(2a^2-4a+6)$
1. $3a^3-a^2+18a$
2. $6a^2-12a+18$
3. $5a^3-a^2+9a$
4. $6a^3-12a^2+18a$
Grade 9 Polynomials and Rational Expressions CCSS: HSA-APR.A.1
$(-4m-n)-(2m+3n)$
1. $-2m-4n$
2. $-6m-4n$
3. $-6m+2n$
4. $-8m-2n$
Grade 9 Quadratic Equations and Expressions CCSS: HSA-REI.B.4, HSA-REI.B.4b
Solve for $x$.
$3x^2-4=8$
1. x = -1, 1
2. x = 12
3. x = 4
4. x = -2, 2
5. x = 3
Grade 11 Quadratic Equations and Expressions
What is the simplified form of $(3x^3y^-4)^-2?$
Exponent answers must have positive exponents in them.
1. $y^8/(6x^-2)$
2. $(9y^8)/(x^6)$
3. $(y^8)/(9x^6)$
4. $(y^8)/(9x^-6)$
Grade 12 Polynomials and Rational Expressions CCSS: HSA-APR.A.1
$1/(x^2-5x)+x/(x-5)=$
1. $(x^2+1)/(x(x-5))$
2. $(x+1)/(x-5)$
3. $(x-1)/(x-5)$
Grade 9 Polynomials and Rational Expressions CCSS: HSA-APR.D.7
Multiply the rational expressions and simplify as much as possible.
$(3x^2)/(4x^3)*(-2x)/6$
1. $-1/4$
2. $-x/4$
3. $(6x)/24$
4. $x^3/x^2$
Grade 11 Exponents
Simplify. Answer must only have positive exponents.

$(x^-3 * y^-4 * y^2 *x^1) / (x^5 * y^2)$
1. $(x^-2 * y^-2)/(x^5 * y^2)$
2. $(y^2 * x)/(x^8 * y^6)$
3. $1 / (x^8 * y^6)$
4. $1 / (x^7 * y^4)$
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.D.7
$(x^2-64)/(x(x+8))*x/(x-8)$ =
1. $1 , \ \ x!=-8,0,8$
2. $(x^3-64x)/((x+8)(x-8)), \ \ x!= 0$
3. $(x^2-8)/(x^2-64), \ \ x!= 0$
Grade 10 Polynomials and Rational Expressions CCSS: HSA-APR.A.1
What is the difference $(x^4 - 3x^2 + 4x + 7) - (x^4 - 6x^3 + 4x)?$
1. $3x^3 + 7$
2. $6x^3 - 3x^2 + 7$
3. $6x^3 - 3x^2 + 8x + 7$
4. $3x^3 + 8x + 7$
Grade 9 Polynomials and Rational Expressions
Find the greatest common factor of the terms in the polynomial.

$9x^4 + 12x^3 +6x$
1. $2x^2$
2. $3x$
3. $6x^3$
4. $9x^4$
Grade 9 Polynomials and Rational Expressions CCSS: HSA-APR.D.6, HSA-APR.D.7
Simplify. $((x+5)(2x-1))/(2x(x+1)^2)*(x(x+1))/(2x-1)$
1. $1/2$
2. $x+5$
3. $1/(2(x+1)$
4. $(x+5)/(2(x+1)$
5. $(x+5)/(2x)$
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.A.1
Which polynomial has the factorization $(x - 10)(x^2 + 10x + 100)?$
1. $x^3 - 1000$
2. $x^3 - 100$
3. $x^3 + 100$
4. $x^3 + 1000$
Grade 9 Polynomials and Rational Expressions CCSS: HSA-APR.D.7
Grade 9 Algebraic Expressions
Simplify the expression.
$9y ^2 - 2y - 3y^2 + 5y$
1. $12 y^2 + 3y$
2. $6y^2 + 3y^2$
3. $6 y^2 + 3y$
4. $6y^2 + 7y$
Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.D.6
What is the quotient of $(x^3 - 3x^2 + 4x - 6) and (x - 2)?$
1. $x^2 - x + 2$
2. $x^2 - x + 3$
3. $x^2 - x + 2 + (2)/(x - 2)$
4. $x^2 - x + 2 - (2)/(x - 2)$
Grade 9 Polynomials and Rational Expressions
What is the least common denominator?
$1/(x+1)+4/((x+1)(x-1)$
1. $(x+1)(x-1)$
2. $(x+1)(x+1)$
3. $(x-1)$
4. $(x+1)$
Grade 9 Polynomials and Rational Expressions CCSS: HSA-APR.A.1
$(3x^2y^3+xy^2)(x^4y-2x^2y^2)$
1. $3x^4y^2-6x^4y^6+x^5y^2-2x^3y^4$
2. $3x^6y^4-6x^4y^5+x^5y^3-2x^3y^4$
3. $3x^6y^4-6x^4y^5+x^4y^4-2x^2y^2$
4. $3x^4y^6-6x^5y^4+x^3y^5-2x^4y^3$
Grade 9 Polynomials and Rational Expressions CCSS: HSA-APR.A.1
$(2x+3)(5x-8)$
1. $10x^2+x-24$
2. $10x^2-31x-24$
3. $10x^2-x-24$
4. $7x^2+10x-5$
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