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# Polynomials and Rational Expressions Questions - All Grades

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Grade 10 Polynomials and Rational Expressions
Match each factored expression with its corresponding expanded form.
 __ $2(x-5)^2$ A. $3x^3-27x^2$ __ $3x^2(x-9)$ B. $2x^2 + 2x-24$ __ $2(x+4)(x-3)$ C. $x^3-x^2-5x+5$ __ $(x^2-5)(x-1)$ D. $2x^2 -20x+50$
Grade 9 Polynomials and Rational Expressions CCSS: HSA-APR.A.1

$(3x^2+3x+1) + (x^2+x+5)$
1. $4x^2+4x+6$
2. $3x^2-2x+4$
3. $4x^2-4x-6$
4. $2x^2+2x-4$
Grade 9 Polynomials and Rational Expressions
Which of the following best classifies $5a^4+7a^3-2a ?$
1. Cubic polynomial
2. Quartic binomial
3. Quartic trinomial
4. Quintic polynomial
Grade 9 Polynomials and Rational Expressions
What is the best classification of the polynomial $6 ?$
1. Constant monomial
2. Constant binomial
3. Linear monomial
4. This is not a polynomial.
Grade 11 Polynomials and Rational Expressions
Factor the following polynomial.

$x^3-x^2-8x+12$
1. $(x+3)(x-2)^2$
2. $(x+3)(x-2)(x+1)$
3. $(x-3)(x+1)(x-5)$
4. $(x-1)(x-2)(x+4)$
Grade 10 Polynomials and Rational Expressions CCSS: HSA-APR.D.7
Multiply. Simplify if possible. $(2x^2)/5*25/x^3$
1. $(2x^2 + 25)/(5x^3)$
2. $(2x^5)/(125), \ \ x!=0$
3. $10/x$
4. $x/10, \ \ x!=0$
Grade 9 Polynomials and Rational Expressions CCSS: HSA-APR.A.1
$(4a^2 + b^2 + a - 5c + 7) + (c^2 - 5 + a - 3b^2 - 6a^2)$
1. $4a^2 -3b^2 -4c^2 + 2a + 7$
2. $10a^2 + 4b^2 +c^2 + 2a + 5c + 12$
3. $4a^2c^2 + ab^2 - 8b^2c - a^2 - 5a$
4. $-2a^2 - 2b^2 + c^2 + 2a - 5c + 2$
Grade 10 Polynomials and Rational Expressions
Given: $(5x + 6)(8x - 4)$

What is the product of the given?
1. $13x + 2$
2. $40x - 24$
3. $40x^2 + 24$
4. $40x^2 - 20x + 48x - 24$
Grade 9 Polynomials and Rational Expressions
Grade 9 Polynomials and Rational Expressions
Grade 9 Polynomials and Rational Expressions
Grade 9 Polynomials and Rational Expressions CCSS: HSA-APR.A.1
Subtract the polynomials.
$(-3z^2 + 9z -4) - (4z^2 -5 + z)$
1. $-7z^2 + 8z +1$
2. $-z^2 + 8z - 9$
3. $z^2 + 10z -9$
4. $7z^2 +4z -3$
Grade 11 Polynomials and Rational Expressions CCSS: HSN-CN.C.9
Looking at the graph of a quadratic polynomial, roots or zeros correspond to where the graph crosses the x-axis. When the graph just touches the x-axis, this corresponds to a double root. The Fundamental Theorem of Algebra states that a quadratic polynomial will always have 2 roots. How is this reconciled with a quadratic polynomial whose graph does not intersect the x-axis?
1. Quadratic polynomials always intersect the x-axis.
2. If a quadratic polynomial doesn't cross the x-axis it is no longer a polynomial, and the Fundamental Theorem of Algebra no longer applies.
3. When a quadratic polynomial doesn't cross the x-axis, this simply implies that its roots are complex with non-zero imaginary parts.
4. Simply translate the quadratic polynomial till it does cross the x-axis.
Grade 9 Polynomials and Rational Expressions CCSS: HSA-APR.A.1
$(5z^2 - 4z + 4) + (-3z - z^2 + 5)$
1. $2z^2 - 5z + 9$
2. $6z^2 + 7z + 9$
3. $8z^2 + 5z + 9$
4. $4z^2 - 7z + 9$
Grade 9 Polynomials and Rational Expressions
Which expression is not considered a polynomial?
1. $x^4+2x^2+1$
2. $x^2 + 2^x$
3. $x^3 -.5x^2 - 1$
4. $4$
Grade 9 Polynomials and Rational Expressions
The following expression is a
$x^3 + 2x^2- 5x - 10$
1. monomial.
2. binomial.
3. trinomial.
4. polynomial.
Grade 9 Polynomials and Rational Expressions CCSS: HSA-APR.A.1
Multiply the monomials.
$3x^7 * 2x^4$
1. $6x^11$
2. $5x^11$
3. $6x^28$
4. $5x^28$
Grade 11 Polynomials and Rational Expressions CCSS: HSN-CN.C.9
Jeremy is working with the Fundamental Theorem of Algebra, and thinks he's found an exception. Looking at $f(x) = 4(x-1)^2$, this will result in only one root, $x=1$. Therefore, despite this being a second degree polynomial, there is only one root. Is this correct?
1. Yes, this is a known exception.
2. No, this is not a polynomial, it is a quadratic function.
3. No, if the quadratic formula is used, the other root is found.
4. No, this root has multiplicity of 2, which means it counts as two roots.
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