Polynomial Operations

Match

Match the following

• 7

• $$3x-5$$

• $$-9a^2b^3-ab+4b^3-6$$

Monomial

Binomial

Polynomial

• Monomial

• Binomial

• Polynomial

Open Ended

Type your own monomial.

Multiple Choice

$$7x^{\frac{1}{2}}+2y-2y^2+17$$

Determine if the expression above is a polynomial or not.

• Polynomial

• Not Polynomial

Not a Polynomial

7x^1/2 + 2y - 2y² + 17

Not an integer(whole number)

Exponents must be positive integers {0, 1, 2, 3, 4,...}

Some text here about the topic of discussion

Multiple Choice

Which expression is equivalent to

$$\left(-2a^3b+35a^2b^2+17ab^3-5\right)+\left(14ab^3-3a^3b-15a^2b^2+5\right)$$

• $$12ab^3+38a^3b^3+2a^3b^5$$

• $$-5a^3b+20a^2b^2+31ab^3$$

• $$12a^3b^3+32a^5b^3+2a^3b^5$$

• $$5a^3b-20a^2b^2+3ab^3-10$$

Multiple Choice

Which expression is equivalent to

$$\left(10x^5y^2-8x^3y+13xy^2-y^4\right)+\left(-12x^5y+4xy^2-2x^3y+10\right)$$

• $$-2x^5y^2-10x^3y+17xy^2-y^4+10$$

• $$2x^5y-10x^3y-9xy^2-y^4+10$$

• $$10x^5y^2-12x^5y-10x^3y+17xy^2-y^4+10$$

Multiple Choice

Which expression is equivalent to

$$\left(6x^3y-2x^2y^2-7xy^3+19\right)-\left(-8xy^3+14x^3y-13x^2y^2+10\right)$$

• $$-8x^3y+11x^2y^2+xy^3+9$$

• $$8x^3y-11x^2y^2-xy^3-9$$

• $$20x^3y-15x^2y^2-15xy^3-29$$

• $$-20x^3y+15x^2y^2+15xy^3-29$$

Multiple Choice

Which expression is equivalent to

$$\left(-5a^3b+a^2b^2-9ab^3-5\right)-\left(8a^3b+a^2b^2-9ab^3+10\right)$$

• $$-13a^3b+2a^2b^2-18ab^3+5$$

• $$13a^3b-2a^2b^2+18ab^3-5$$

• $$13a^3b+15$$

• $$-13a^3b-15$$

Multiple Choice

Which expression is equivalent to

$$\left(3a^3b-5a^2b^2+7ab^3-11\right)-\left(11a^2b^2+7a^3b-5ab^3+3\right)$$

• $$-10a^3b+16a^2b^2-2ab^3+8$$

• $$10a^3b-16a^2b^2+2ab^3-8$$

• $$4a^3b+16a^2b^2-12ab^3+14$$

• $$-14a^3b-16a^2b^2+12ab^3-14$$

Multiple Choice

$$\left(x\right)\left(x^3\right)=$$

• $$x^4$$

• $$2x^3$$

• $$x^3$$

• $$x^2$$

Multiple Choice

$$\left(x^2y\right)\left(x^4\right)=$$

• $$xy^6$$

• $$x^6y$$

• $$x^6$$

• $$x^7$$

Multiple Choice

$$\left(a^2b^3\right)\left(ab\right)=$$

• $$a^4b^3$$

• $$a^3b^4$$

• $$a^2b^3$$

• $$ab^4$$

Multiple Choice

(4a)(6b)

• $$24ab$$

• $$24a^2$$

• $$10ab$$

• $$2ab$$

Multiple Choice

$$-3x\left(xy^2\right)$$

• $$3x^2y^2$$

• $$-3xy^2$$

• $$-3x^2y^2$$

• $$-2xy^2$$

Multiple Choice

$$\left(-\frac{1}{4}xy\right)\left(-x^4y^2\right)$$

• $$-\frac{1}{4}x^5y^3$$

• $$\frac{1}{4}x^5y^3$$

• $$-\frac{1}{4}x^2y$$

• $$\frac{1}{4}x^2y^{ }$$

Multiple Choice

Which expression is equivalent to

$$\left(5a+6b\right)\left(2a^2+3ab-b^2\right)$$

• $$-10a^3-27a^2b-23ab^2-6b^3$$

• $$-10a^3-27a^2b-13ab^2+6b^3$$

• $$10a^3+27a^2b+13ab^2-6b^3$$

• $$10a^3+27a^2b+23ab^2+6b^3$$

Multiple Choice

Which expression is equivalent to

$$\left(2a^2+3ab-b^2\right)\left(-2a+3b\right)$$

• $$4a^3+7ab^2-3b^3$$

• $$4a^3+12a^2b+7ab^2+3b^3$$

• $$-4a^3-12a^2b+11ab^2-3b^3$$

• $$-4a^3+11ab^2-3b^3$$

Multiple Choice

Which expression is equivalent to

$$\left(x+y\right)\left(x-2y\right)\left(2x+y\right)$$

• $$-2x^3+3x^2y+2y^3$$

• $$2x^3-x^2y-5xy^2-2y^3$$

• $$2x^3+x^2y+5xy^2-2y^3$$

• $$2x^3+3x^2y+5xy^2+2y^3$$

Multiple Choice

$$x^{-3}$$

• $$x^3$$

• $$\frac{1}{x^3}$$

Multiple Choice

$$xy^{-1}$$

• $$\frac{x}{y}$$

• $$\frac{1}{xy}$$

• $$\frac{y}{x}$$

Multiple Choice

$$x^2y^{-3}z^{-1}$$

• $$\frac{x^2y^3}{z}$$

• $$x^2y^3z$$

• $$\frac{x^2}{y^3z}$$

Multiple Choice

$$\left(xy\right)^{-1}$$

• $$\frac{x}{y}$$

• $$\frac{1}{xy}$$

• $$\frac{y}{x}$$

Multiple Choice

$$3^{-1}$$

• 3

• $$\frac{1}{3}$$

Multiple Choice

$$\frac{1}{x^{-1}}$$

• $$\frac{1}{x}$$

• $$x$$

Multiple Choice

$$\frac{x^{-1}}{y^{-1}}$$

• $$\frac{x}{y}$$

• $$\frac{y}{x}$$

Multiple Choice

$$\frac{b^8}{b^5}$$

• $$\frac{1}{b^3}$$

• $$b^3$$

Multiple Choice

$$\frac{x^2}{x^3}$$

• $$\frac{1}{x}$$

• $$x$$

Multiple Choice

$$\frac{z}{z^{-1}}$$

• $$1$$

• $$z^2$$

• $$z$$

Multiple Choice

$$\frac{15xy^4z^7}{5xy^3z^5}$$

• $$10yz^2$$

• $$3yz^2$$

• $$10xyz^2$$

• $$3xyz^2$$

Multiple Choice

$$\frac{4xy^4z^7}{12x^2y^3z^5}$$

• $$\frac{3x}{yz^2}$$

• $$3xyz^2$$

• $$\frac{xyz^2}{3}^{ }$$

• $$\frac{yz^2}{3x}$$

Multiple Choice

$$\frac{5xy^4z^8}{5y^5z^5}$$

• $$0$$

• $$\frac{5x}{yz}$$

• $$\frac{xz^3}{y}$$

• $$\frac{y}{xz^3}$$