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Polynomials and Rational Expressions Questions - All Grades

You can create printable tests and worksheets from these Polynomials and Rational Expressions questions! Select one or more questions using the checkboxes above each question. Then click the add selected questions to a test button before moving to another page.

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Grade 9 Polynomials and Rational Expressions

A polynomial that has two terms.

monomial
trinomial
binomial

Grade 9 Polynomials and Rational Expressions CCSS: HSA-APR.A.1

Add.

$(3x^2 + 4xy + y^2 + 12x - 6y) + (-2x^2 + 2xy + 9y^2 - 5x + 8y)$

$x^2 + 6xy + 10y^2 + 7x + 2y$
$5x^2 + 6xy + 10y^2 + 17x+ 14y$
$3x^2 + 10y^2 + 11x + 4y$
$5x^2 + 7xy + 9y^2 -14y$

Grade 10 Polynomials and Rational Expressions

Identify the property used to begin the factoring of the given polynomial.

Given:

$7p^3r - 5t^3s - 21p^2r -10s^3t^3$

Step 1:

$7p^3r- 21p^2r - 5t^3s -10s^3t^3$

Associative Property
Commutative Property
Distributive Property
Substitution Property

Grade 11 Polynomials and Rational Expressions

Use the GCF of the terms to factor the polynomial.

Given:

$23x^4 + 46x^3$

$x^3(23x+46)$
$23x^3(x+2)$
$23x^4(x+2)$
$23x(x^3+2x^2)$

Grade 9 Polynomials and Rational Expressions CCSS: HSA-APR.A.1

$3x^2+x-5$ is classified as which of the following?
(select all that apply)

Monomial
Binomial
Trinomial
Polynomial
None of the above

Grade 10 Polynomials and Rational Expressions CCSS: HSA-APR.D.7

Divide. Simplify if possible.

$(x^2-12x+36)/(2x-12)-:(5x-30)/10$

$x-6, \ \ x!=6$
$1/(x-6)$
$(x-6)^2/4, \ \ x!= 6$
$1, \ \ x!=6$

Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.D.6

Use synthetic division to divide the polynomials:

$(x^2+2x-63)/(x+9)$ .

$x-7$
$x+7$
$x^2-7$
$x^2+3x-54$

Grade 9 Polynomials and Rational Expressions CCSS: HSA-APR.A.1

Subtract.

$(3a^3 -5a^2 +11) - (6a^3 - a - 2)$

$3a^3 - 5a^2 - a +9$
$-3a^3 - 4a^2 + 13$
$9a^3 - 5a^2 - a + 9$
$-3a^3 - 5a^2 + a + 13$

Grade 11 Polynomials and Rational Expressions CCSS: HSN-CN.C.9

What is the maximum number of complex roots with non-zero imaginary part,

$a+bi, b!=0$ , the polynomial

$4x^5 - 5x + 6$ can have?

Grade 10 Polynomials and Rational Expressions CCSS: HSA-APR.D.7

Add. Simplify the result if possible.

$5/(15x)+6/(15x)$

$11/(15x)$
$1, \ \ x!=0$
$(15x)/11, \ \ x!=0$
$11/(30x)$

Grade 10 Polynomials and Rational Expressions CCSS: HSA-APR.D.7

Subtract. Simplify if possible.

$(9x^2)/(x-1)-(9x)/(x-1)$

$(9x(x+1))/(x+1), \ \ x!=1$
$(9x)/(x-1)$
$0, \ \ x!=1$
$9x, \ \ x!=1$

Grade 10 Polynomials and Rational Expressions

Factor by grouping.

$15x^3-6x^2-25x+10$

$(5x-5)(3x^2-2)$
$(x-2)(15x^2-5)$
$(15x-2)(x^2-5)$
$(5x-2)(3x^2-5)$

Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.D.7

Add and simplify.

$\ (x^2-4x+3)/(x^2+4x-5)+(x^2+4x+3)/(x^2+6x+5)$

$(2x)/(x+5), \ x!= -1, 1$
$(2x^2+6)/(2x^2+10x), \ x!= 0, -5$
$(10(4x^2+3x))/(24x^2-10x-25)$
$(6)/(x^2+6x+5) , \ x!= 1$

Grade 9 Polynomials and Rational Expressions

Find the greatest common factor of

$6xyz + 12x^2y - 3yz^2$ .

$3xy$
$6yz$
$3y$
$2x^2y$

Grade 10 Polynomials and Rational Expressions

Simplify the expression.

$(9x^3+2)+(2x^3-1)$

$11x^3+1$
$7x^3+1$
$9x^3-1$
$10x^3-1$

Grade 11 Polynomials and Rational Expressions

To simplify the rational expression

$(x+6)/(x^2+5x-6$ , what is the factored form of the trinomial in the denominator?

$(x+6)(x-1)$
$(x-6)(x+1)$
$(x-6)(x-1)$
$(x+6)(x+1)$

Grade 9 Polynomials and Rational Expressions

$3x+9$ is an example of a

linear monomial.
quadratic binomial.
constant binomial.
linear binomial.
polynomial polynomial.

Grade 9 Polynomials and Rational Expressions

Factor using the greatest common factor.

$16x^8-32x^7+12x^2$

$12x^2(4x^6-8x^5+1)$
$4x^2(4x^6-8x^5+3)$
$4x(4x^8-8x^7+3x^2)$
$x^2(16x^6-32x^5+12)$

Grade 10 Polynomials and Rational Expressions CCSS: HSA-APR.D.7

Multiply. Simplify if possible.

$(2x-2)/x * (8x^2)/(3x-3)$

$3/(16x), \ \ x!= 1$
$(3(x+1)^2)/(4x^2), \ \ x!=1$
$(16x)/3, \ \ x!= 0,1$
$(16x-1)/(3x^2), \ \ x!=1$

Grade 10 Polynomials and Rational Expressions

Name the polynomial by degree and the number of terms.

$9x^3-10x^5+26$

Quintic Trinomial
Quintic Monomial
Quintic Binomial
Quintic Polynomial

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Polynomials and Rational Expressions Questions - All Grades