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Tenth Grade (Grade 10) Polynomials and Rational Expressions Questions

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

Multiply. Simplify if possible.

$(2x^2)/5*25/x^3$

$(2x^2 + 25)/(5x^3)$
$(2x^5)/(125), \ \ x!=0$
$10/x$
$x/10, \ \ x!=0$

Grade 10 Polynomials and Rational Expressions

Given:

$(5x + 6)(8x - 4)$

What is the product of the given?

$13x + 2$
$40x - 24$
$40x^2 + 24$
$40x^2 - 20x + 48x - 24$

Grade 10 Polynomials and Rational Expressions CCSS: HSA-SSE.A.2

Factor the expression.

$x^4 - y^4$

$(x - y)^4$
$(x^2 + y^2)(x + y)(x - y)$
$(x^2 + y^2)(x^2 - y^2)$
Can't be factored

Grade 10 Polynomials and Rational Expressions

Which of the following represents the simplified polynomial expression, given

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

$9x^4y^6+21x^2y^3-12x^2y^4$
$6x^2y^2+10x^2y^3-7x^2y^4$
$9x^4y^3+21x^3y^4-12x^2y^5$
$6x^4y^3+10x^3y^4-7x^2y^5$

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

Divide. Simplify if possible.

$(x+3)/(7x) -: (x-3)/(21x)$

$(3(x+3))/(x-3), \ \ x!=0$
$3, \ \ x!=0, 3$
$((x+3)(x-3))/(147x^2), \ \ x!=3$
$(3(x-3))/(x+3), \ \ x!=0,3$

Grade 10 Polynomials and Rational Expressions

Write the expression

$(x + 5)(x + 2)$ as a polynomial in standard form.

$x^2 + 3x + 10$
$x^2 - 3x + 7$
$x^2 +7x + 10$
$x^2 +3x -3$

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 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 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 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 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

Grade 10 Polynomials and Rational Expressions CCSS: HSA-SSE.B.3, HSA-SSE.B.3a

Factor:

$9y^2 - 25$

$(3y + 5) (3y - 5)$
$(9y + 5) (9y - 5)$
$(9y - 25) (y + 1)$
$(3y + 30) (3y - 5)$

Grade 10 Polynomials and Rational Expressions

What type of polynomial has two terms?

monomial
binomial
trinomial
polynomial

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

Step 1 :

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

Step 2:

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

Which of the following is the GCF for one of the pairs of terms in step 2?

There are no common factors.
$p^3r$ is a factor of $(7p^3r- 21p^2r)$ .
$-5s$ is a factor of $( - 5t^3s -10s^3t^3)$ .
$7p^2r$ is a factor of $(7p^3r- 21p^2r)$ .

Grade 10 Polynomials and Rational Expressions

Select the polynomial that is written in standard form.

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

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

Divide. Simplify if possible.

$(x^2+x-90)/(x-3) -: (x-9)/(x^2-13x+30)$

$x-9, \ \ x!=3,9,10$
$((x+10)(x-9)^2)/((x-10)(x-3)^2), \ \ x!=9$
$((x-9)(x+10))/(x-10), \ \ x!=3,9$
$x^2-100, \ \ x!=3,9,10$

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Tenth Grade (Grade 10) Polynomials and Rational Expressions Questions