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Tenth Grade (Grade 10) Polynomials and Rational Expressions Questions

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Grade 10 Polynomials and Rational Expressions

Step 1 :

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

Step 2:

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

Factoring by grouping, which is illustrated in step 2, is actually applying which of the following properties?

Associative Property
Commutative Property
Distributive Property
Substitution Property

Grade 10 Polynomials and Rational Expressions CCSS: HSA-APR.D.6

Simplify.

$(x - y)/(x^2 - 2xy + y^2)$

$x + y$
$xy$
$1/(x-y)$
$x - y$

Grade 10 Polynomials and Rational Expressions CCSS: HSA-APR.D.6

Divide:

$(x^2-3x-28)-:(x+4)$

$x-7$
$x+4$
$x+7$
$x-4$

Grade 10 Polynomials and Rational Expressions CCSS: HSA-APR.A.1

Find the product:

$(n+3)(2n^2-4n-2)$

$n^3+6n^2-12n-6$
$2n^3+2n^2-14n-6$
$2n^3+2n^2-10n-6$
$2n^3-2n^2+14n-6$

Grade 10 Polynomials and Rational Expressions

The product of a monomial and a trinomial is (a)

monomial.
binomial.
trinomial.
coefficients.

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

Add. Simplify if possible.

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

$(-3(x-4))/((x+2)(x-1))$
$3/(x-1), \ \ x!= -2$
$(3(x+5))/(x+2)(x-1)$
$3/(x+2), \ \ x!=1$

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

Subtract. Simplify if possible.

$(2x-5)/(x-5) - (x^2 +2x)/(x^2-3x-10)$

$(3x-5)/(x-5), \ \ x!= -2$
$(x-10)/(x-5), \ \ x!= -2$
$1, \ \ x!= -2, 5$
$(-5)/(x+2), \ \ x!=5$

Grade 10 Polynomials and Rational Expressions

$81z^2-x^2$ =

$(9z-x)^2$
$81(z-x)(z+x)$
$(9z-x)(9z+x)$

Grade 10 Polynomials and Rational Expressions CCSS: HSA-APR.C.4

Which one of the following is NOT true?

$(x+2)(x-2)=x^2-4$
$(30+2)(30-2)=900-4$
$(2x+1)(2x-1)=4x^2-1$
$(a+b)(a-b)=a^2-b^2$
$(2a+3b)(2a-3b)=2a^2-3b^2$

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

Factor.

$x^2 + 5x + 6$

Grade 10 Polynomials and Rational Expressions

Classify as true or false.

$(8a^2b+2b^2)/(2b)=4a^2+b$

True
False

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

Add. Simplify if possible.

$(3x)/(x(x+2)) + (x-1)/(x-2)$

$1, \ \ x!= -2, 0, 2$
$(x+2)/(x-2), \ \ x!= -2, 0$
$(x^2+4x-8) / ((x+2)(x-2)), \ \ x!= 0$
$(x^3 + 4^2 - 8x)/((x+2)(x-2)), \ \ x!=0$

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

Which one of the following is equivalent to

$x^4-x^2-30$ ?

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

Grade 10 Polynomials and Rational Expressions

Order the terms by the degree of the variable in the expression

$52 + x^3 + y^2 + 20xy$ .

$x^3 + y^2 + 20xy + 52$
$y^2 + x^3 + 52 + 20xy$
$20xy + x^3 + y^2 + 52$
$52+ 20xy + x^3 + y^2$

Grade 10 Polynomials and Rational Expressions CCSS: HSA-APR.A.1

Combine the polynomials:

$(3x^2-x+8y)+(4x^2-3x-5y)$

Grade 10 Polynomials and Rational Expressions

Which of the following expressions is written in standard form with A=3, B= -4 and C= 3?

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

Grade 10 Polynomials and Rational Expressions

Factor the polynomial by grouping:

$x^3-2x^2-16x+32$

Grade 10 Polynomials and Rational Expressions CCSS: HSA-APR.A.1

Find the product.

$(3x+1)(5x^3+2x^2-8x)$

$15x^4+11x^3-22x^2-8x$
$15x^3+11x^2-22x-8$
$8x^4-11x^3+22x^2+8x$
$15x^4+x^3+26x^2-8x$

Grade 10 Polynomials and Rational Expressions

Order the terms by the degree of the variable in the expression

$3y - 4x^3 y^2 + 8x^6 y^5 - 9x^2 + 12x$ .

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

Grade 10 Polynomials and Rational Expressions

Evaluate

$(2x^2+5)/ (2y^2-2)$ if

$x=2.5$ and

$y=-1.5$ .

17.5 / -5
7
9
-7

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Tenth Grade (Grade 10) Polynomials and Rational Expressions Questions