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Ninth Grade (Grade 9) Polynomials and Rational Expressions Questions

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Grade 9 Polynomials and Rational Expressions

Classify the following polynomial.

$2x^3 + 8x^2 + 9x + 4$

Quartic trinomial
Cubic binomial
Quadratic trinomial
Cubic polynomial

Grade 9 Polynomials and Rational Expressions

What is the degree of the following polynomial?

$3x^2y^4 - 2x^3y^5$

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.

$5x - 7 = 8$

Step 1:	$5x-7+7$	$= \ \ 8$
Step 2:	$5x$	$= \ \ 8$
Step 3:	$\(5x)/5$	$= \ \ 8/5$
Step 4:	$x$	$= \ \ 8/5$

It is correct.
Step 1 is incorrect because you should divide by 5 first.
Step 1 is incorrect because you have to add 7 to both sides.
Step 3 is incorrect because you only need to cancel the 5, not divide.

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

Subtract the polynomials.

$(6x^3 - 4x^2y + 9xy^2 - 2y^3) - (xy^2 - 3x^2y + 4x^3 - 7y^3)$

$5x^3 - x^2y + 5xy^2 + 5y^3$
$2x^3 - x^2y + 8xy^2 +5y^3$
$2x^3 - 7x^2y + 8xy^2 - 9y^3$
$5x^3 -5x^2y + 12xy^2 - 9y^3$

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.

$2x + 3 = 4x$

Step 1:	$\ \ \$	$\ \ \$
Step 2:	$3$	$= \ \ 2x$
Step 3:	$3/2$	$= \ \ (2x)/2$
Step 4:	$3/2$	$= \ \ x$

Subtract 3 from both sides.
Add 3 to both sides.
Subtract 2x from both sides.
Divide by 2x on both sides.

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

$(2x+3)(5x-8)$

$10x^2+x-24$
$10x^2-31x-24$
$10x^2-x-24$
$7x^2+10x-5$

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

$(3x^2y^3+xy^2)(x^4y-2x^2y^2)$

$3x^4y^2-6x^4y^6+x^5y^2-2x^3y^4$
$3x^6y^4-6x^4y^5+x^5y^3-2x^3y^4$
$3x^6y^4-6x^4y^5+x^4y^4-2x^2y^2$
$3x^4y^6-6x^5y^4+x^3y^5-2x^4y^3$

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

$(10p^4+p^3-4p^2-8)-(-12p^4+5p^3-2p+3)$

$22p^4-4p^3-4p^2+2p-5$
$-2p^4-4p^3-4p^2+2p-5$
$-2p^4+6p^3-6p^2+2p-11$
$22p^4-4p^3-4p^2+2p-11$

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

Add.

$(-4x^2 + 7x -11) + (6x^3 -7x +10)$

$2x^2 + x -1$
$6x^3 - 4x^2 -1$
$-2x^3 - x + 1$
$10x^2 + 14x + 21$

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 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 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.

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Ninth Grade (Grade 9) Polynomials and Rational Expressions Questions