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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 CCSS: HSA-APR.A.1

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

$6x^2+4x-10$
$6x^2+16x-10$
$-x+3$
$6x^2-4x+10$

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

$3x(x+5)$

$3x+15x$
$3x^2+15x$
$18x$
$3x^3+15x^2$

Grade 9 Polynomials and Rational Expressions

$5x^3 + 4x + 1$ is best classified as which of the following?

Cubic monomial
Quintic trinomial
Cubic trinomial
Quartic polynomial

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

Multiply.

$3x^2 * (4x^3 - 7)$

$12x^6$
$4x^3 + 3x^2 - 7$
$7x^5 - 4x^2$
$12x^5 - 21x^2$

Grade 9 Polynomials and Rational Expressions

A trinomial is

an expression with 1 term.
an expression with 2 terms.
an expression with 3 terms.
an expression with more than 3 terms.

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

Multiply. Simplify fully.

$(4y^3) (7y^5)$

$11y^8$
$28y^3$
$4y^3 7y^5$
$28y^8$

Grade 11 Polynomials and Rational Expressions

$81 - 9k^2$

$(3k - 9)(3k - 9)$
$(9 + 3k)(9 - 3k)$
$(3k + 9)(3k - 9)$
$(9 + 3k) (9 + 3k)$

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

$(7n^5-3n+4n^2)+(2n^2+5n^5+8n)$

$12n^5+6n^2+5n$
$9n^5+2n^2+12n$
$5n^5-2n^2+4n$
$12n^5-6n^2-4n$

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

Add. Your answer should be fully simplified.

$(2x + 5) + (4x + 7)$

$18x$
$8x^2 + 34x + 35$
$6x + 12$
$2x + 4x + 5 + 7$

Grade 11 Polynomials and Rational Expressions CCSS: HSA-APR.A.1

Tommy is building a rectangular garden. His dimensions are

$5x$ and

$5x-4$ . Find the area of the rectangular garden he is building in terms of

$x$ . (area = lw)

$25x^2-20x$
$25x^2-4$
$25x^2 +5x - 4$
$25x - 20$

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

$(13x-3)(5-6x)$

$-18x^2+65x-78$
$-65x^2+18x-15$
$-38x^2+78x-15$
$-78x^2+83x-15$

Grade 9 Polynomials and Rational Expressions

Subtract the two polynomials.

$(4a^2 - 3c^2 - a + 7b -13) - (3a^2 +5b^2 + 2b - 3c +3)$

$a^2 + 5b^2 - 3c^2 -a +5b -3c -10$
$a^2 - 8c^2 -3a + 10b -16$
$a^2 - 5b^2 - 3c^2 - a + 5b + 3c - 16$
$a^2 +5b-16$

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

Is the solution to the equation correct? If not, identify which step contains an error and why this step is incorrect.

$3x - 2 = 10 - x$

Step 1:	$3x-2+x$	$= \ \ 10-x+x$
Step 2:	$4x-2$	$= \ \ 10$
Step 3:	$4x-2+2$	$= \ \ 10+2$
Step 4:	$4x$	$= \ \ 12$
Step 5:	$(4x)/4$	$= \ \ 12$
Step 6:	$x$	$= \ \ 12$

It is correct.
Step 1 is incorrect because you have to start with getting rid of the -2.
Step 1 is incorrect because you should divide by 3 on both sides.
Step 5 is incorrect because you have to divide by 4 on both sides.

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

What is

$4x^3-2x^2+7x+5$ divided by

$(x+2)?$

$(4x^2-10x+27)-49/(x+2)$
$(4x^2-10x+27)$
$(4x^2-10x+27)+59/(x+2)$
$(4x^2-10x+27)-59/(x+2)$

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

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

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

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Polynomials and Rational Expressions Questions - All Grades