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Ninth Grade (Grade 9) Polynomials and Rational Expressions Questions

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Grade 9 Polynomials and Rational Expressions

Write the given polynomial in standard form.

Given:

$4g–g^3 +3g^2 –2$

$–2+4g+3g^2–g^3$
$3g^3 –g^2 +4g–2$
$g^3–3g^2+4g–2$
$–g^3 +3g^2 +4g–2$

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

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

$-2x^3+2x^2+2y$
$3x^3+9x^2-2y$
$3x^3-9x^2+2y$
$-2x^3-2y$

Grade 9 Polynomials and Rational Expressions

A perfect square trinomial is the square of a binomial:

$(a+b)^2 = (a+b)(a+b) = a^2 + 2ab +b^2$ or

$(a-b)^2 = (a-b)(a-b) = a^2 -2ab +b^2$ .

True
False

Grade 9 Polynomials and Rational Expressions

Write the polynomial in standard form.

$4g-g^3+3g^2-2$

$-2+4g+3g^2-g^3$
$g^3-3g^2+4g-2$
$3g^3-g^2+4g-2$
$-g^3+3g^2+4g-2$

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

Add.

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

$2z^4 + 10z^2 - 8z -12$
$8z^4 + 6z^2 -12$
$5z^4 + 3z^3 +10z^2 + 8z + 12$
$5z^4 + 3z^3 + 6z^2 - 12$

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

Subtract.

$(2m^5 + 3m^2 -7) - (4m^4 - 2m^3 + 5m)$

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

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

Simplify the following polynomial expression.

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

$-3x^3+5$
$-3x^3-11$
$3x^3+5$
$3x^3+6$

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

Which fraction equals the product?

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

$(2x - 3)/(3x + 2)$
$(3x + 2)/(4x - 3)$
$(x^2 - 25)/(6x^2 - 5x - 6)$
$(2x^2 + 7x - 15)/(3x^2 - 13x - 10)$

Grade 9 Polynomials and Rational Expressions

Factoring is to express a polynomial as the product of two or more polynomials

Grade 9 Polynomials and Rational Expressions

Which polynomial is written in standard form?

$5x^3 +2x - 9x^2$
$2x - 9x^2 +5x^3$
$5x^3 - 9x^2 + 2x$

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

Multiply.

$2x^3y * (-5x^2y + 9xy - 4y^2 + x -3)$

$-10x^5y^2 + 18x^4y^2 - 8x^3y^3 + 2x^4y - 6x^3y$
$2x^3y - 5x^2y + 9xy - 4y^2 + x - 3$
$-10x^6y + 9x^3y - 4y^2 + 2x^3 - 6$
$-3x^6y^2 + 11x^3y^2 - 2x^3y^2 +2x^4y - x^3y$

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

$(3x^2-6x+2)-(-2x+3x^2+2)$

$-4x$
$6x^2+8x$
$x^2-3x$
$x^2-3x+4$

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

Multiply:

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

$-2x^3+3x^2+x$
$-2x^2+3x+1$
$2x^3-7x^2-7x-2$
$2x^3+x^2-5x+2$
$2x^3-7x^2+5x+2$

Grade 9 Polynomials and Rational Expressions

Simplify the following polynomial by combining like terms.

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

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

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

Multiply.

$(3ab) (-2a^2 + 5ab - b^2)$

$-2a^2 + 8a^2b^2 - b^2$
$a^3b + 8a^2b^2 + 2ab^3$
$3a^2b + 5ab - 3ab^2$
$-6a^3b + 15a^2b^2 - 3ab^3$

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

Subtract.

$(5x^2 - 5xy -y^2 + 9x + 2y - 7) - (3x^2 - 4x + xy - 2y + 4)$

$2x^2 - 6xy -y^2 + 13x +4y - 11$
$8x^2 -4xy - y^2 + 5x - 3$
$2x^2 - 6xy + 5x -11$
$2x^2 - xy - 2y^2 + 9x + 4y -11$

Grade 9 Polynomials and Rational Expressions

$x^2-12x+32$ is an example of a

quadratic binomial.
constant trinomial.
linear monomial.
quadratic trinomial.
quartic polynomial.

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

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

$2x^2 + 2x - 4$
$9x^2 - 5x - 4$
$9x^2 - 2x - 7$
$9x^4 - 5x - 4$

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

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

$2x^2y^3-2x^3y^2-3xy-2$
$2x^3y^2 -2x^2y^3-3xy-2$
$3x^2y^3-3x^3y^2+2xy-2$
$-3x^3y^2 +3x^2y^3-3xy-2$

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

$(x-2)(x+2)$

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

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Ninth Grade (Grade 9) Polynomials and Rational Expressions Questions