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Ninth Grade (Grade 9) Polynomials and Rational Expressions Questions

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Grade 9 Polynomials and Rational Expressions

Find the greatest common factor of the terms in the polynomial.

$9x^4 + 12x^3 +6x$

$2x^2$
$3x$
$6x^3$
$9x^4$

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

A solution to the equation is given, except for one step. Choose the correct action for the missing step.

$(3x)/2 + 4 = 4/5$

Step 1:	$(3x)/2 + 4 - 4$	$= \ \ 4/5 - 4$
Step 2:	$(3x)/2$	$= \ \ -16/5$
Step 3:	$\ \ \$	$\ \ \ \$
Step 4:	$3x$	$= \ \ -32/5$
Step 5:	$(3x)/3$	$= \ \ -32/(5*3)$
Step 6:	$x$	$= \ \ -32/15$

Multiply by 2 on both sides.
Get rid of the fraction on the left hand side.
Multiply by 1/2 on both sides.
Subtract 16/5 from the left hand side.

Grade 9 Polynomials and Rational Expressions CCSS: HSA-APR.D.7

Multiply and simplify.

$((x+5)(2x-1))/(2x(x+1)^2)*(x(x+1))/(2x-1)$

$1/2$
$x+5$
$1/(2(x+1)$
$(x+5)/(2(x+1)$
$(x+5)/(2x)$

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

Multiply the monomial with the trinomial.

$3x^2 * (5y^2 -3y + 6)$

$3x^2 + 5y^2 - 3y + 6$
$15x^2y^2 - 9x^2y + 18x^2$
$8x^2y^2 + 9x^2$
$15x^2y^2 - 3y +6$

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

Subtract:

$(4x^2 - 2x + 8) - ( x^2 + 3x - 2)$

$3x^2 + x + 6$
$3x^2 + x + 10$
$3x^2 - 5x + 6$
$3x^2 - 5x + 10$

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

$(9k+ 4n) - (11k + 6n)$

$2k + 10n$
$-2k -2n$
$2k - 2n$
$20k -10k$

Grade 9 Polynomials and Rational Expressions

What is the degree of the following polynomial?

$6x^3y - 9x^3y^2 + 3x^4 -y + 1$

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

$(x-5)(2x+3)(x+5)$

$2x^3+3x^2-50x-75$
$2x^3+2x^2-15x-25$
$2x^3+2x^2-50x-25$
$2x^3-50x^2+3x-75$

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

Add the polynomials.

$(3x^2-4x+7) + (2x^3-4x^2-6x+5)$

$2x^3+x^2+10x+12$
$2x^3-x^2-10x+12$
$2x^3−x^2+10x-12$
$2x^3−10x+12-x^2$

Grade 9 Polynomials and Rational Expressions

A polynomial that has three terms.

monomial
binomial
exponents
trinomial

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

$-a^2$ is classified as which of the following?
(select all that apply)

Monomial
Binomial
Trinomial
Polynomial
None of the above

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

Multiply.

$3x (5x^3 + 2x^2 - 7x)$

$15x^3 + 3x^2 - 21x$
$15x^4 + 6x^3 - 21x^2$
$5x^3 + 2x^2 - 4x$
$8x^4 +5x^3 - 4x^2$

Grade 9 Polynomials and Rational Expressions

A polynomial that has one term.

exponent
binomial
monomial
trinomial

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

$5x^3-y^2+3x+12y-5$ is classified as which of the following?
(select all that apply)

Monomial
Binomial
Trinomial
Polynomial
None of the above

Grade 9 Polynomials and Rational Expressions

Select the correct term.

$3y - 20$ binomial

$9x - 5y + 10w$ trinomial

$-100y + 8 -w +5x$ polynomial

monomial
polynomial
binomial
trinomial

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

$-2a^2+b-1$ is described as which of the following?
(select all that apply)

Monomial
Binomial
Trinomial
Polynomial
None of the above

Grade 9 Polynomials and Rational Expressions

Simplify the given polynomial.

$(12p^2 + 15p + 3) - (2p^2 + 17p - 2)$

$14p^2 + 32p + 5$
$10p^2 -2p + 5$
$24p^4 +32p - 6$
$-24p^2-234p^3-237p^2-21p + 6$

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

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

Monomial
Binomial
Trinomial
Polynomial
None of the above

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.

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

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

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Ninth Grade (Grade 9) Polynomials and Rational Expressions Questions