A.2 Quiz Review

Preparing for your Exponent Rules and Polynomial Operations QUIZ!

Add your numbers out front. Keep your variables and exponents the same.

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Adding polynomials is like combining like terms.

Multiple Choice

Add the polynomial (-3x + 4) + (8x - 5)

• 5x - 9

• 5x - 1

• 11x - 1

• 11x - 9

• None of these

Multiple Choice

(2x + 5y - z) + (-6x - 4y + 7z)

• -4x +6y + 6z

• 4x + y + 6z

• -4x - y + 6z

• -4x + y + 6z

• None of these

When subtracting polynomials, remember to KEEP, CHANGE, CHANGE. Then do the same thing as adding polynomials.

Multiple Choice

Find the difference.

• 3n²+4n

• -3n²+4n

• 3n²+20n

• 3n²-4n

Multiple Choice

Find the difference.

• 6x²-8x+4

• 4x²-16x+4

• 6x²-16x-4

• 4x²-8x+4

When we multiply polynomials we multiply the numbers and add our exponents together. Make sure all pieces get multiplied.

Multiple Choice

Simplify the expression.
-3x²( 7x² - x + 4)

• -21x⁴ + 3x³ -12x²
• 7x² - x + 4 (-3x²)
• 21x⁴ + 3x³ + 12x²
• -12x² + 3x³ -21x⁴

FOIL
First.
Inner.
Outer.
Last.

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Multiplying binomials: Method 1

Box Method:
One polynomial across top.
One down the side.
Don't forget to combine!

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Multiplying binomials: Method 2

Multiple Choice

Find the product:

(3x – 1)(x + 5)

• 3x² + 4x + 5

• 3x² + 4x − 5

• 3x² + 14x + 5

• 3x² + 14x − 5

Multiple Choice

(2x - 1)(x + 2)

• 2x² + 3x - 2
• 2x² - 5x - 2
• 2x² + 3x + 2
• 2x² - 5x + 2

Multiple Choice

(5x+2)(x²-3x+6)

• 5x³ - 17x² +24x +12
• 5x³ + 17x² - 24x +12
• 5x³ - 13x² + 24x +12
• 5x³ +13x² - 24x - 12

One factor is down the side and the other across the bottom.

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​We can also model this with algebra tiles.

Multiple Choice

What polynomial multiplication problem is shown here using Algebra Tiles? One factor will be on the side and one across the bottom.

• (2x+3)(x+2)

• (x+2)(x+3)

• (2x+4)(x+7)

• (2x+1)(x+3)

Multiple Choice

(2x+3)(x+2) = ?

• x² + 5x + 6

• 2x² + 7x + 6

• 2x² + 6x + 7

• x² + 7x + 5

​Dividing polynomials: Divide each piece of the numerator by your monomial in the denominator. Divide coefficients. Take away exponents.

Multiple Choice

Divide the polynomial by the monomial.

• 2x⁸-8x²-28x
• 2x⁸-2x²-7x
• 8x⁷-8x-28x
• 2x⁷ -2x -7

Let's practice all our exponent rules! Refer to your Exponent Rule Example page as needed.

Multiple Choice

(x⁴)²

• x⁸
• x⁶
• x²
• 8

Multiple Choice

Simplify: $$2m^{-1}$$  

• $$\frac{1}{2m}$$  

• $$\frac{m}{2}$$  

• $$\frac{2}{m}$$  

• $$2m$$  

Multiple Choice

Anything raised to a power of zero is always: 

• 0
• 1
• itself
• negative

Multiple Choice

Simplify: $$\frac{12x^5y^4}{2x^9y}$$  

• $$6x^{-4}y^3$$  

• $$\frac{6y^3}{x^4}$$  

• $$\frac{12y^3}{2x^4}$$  

• $$\frac{6x^{-4}}{y^3}$$  

Multiple Choice

(6x²)(-3x⁵)

• 18x⁷
• -18x⁷
• 18x⁷
• 3x⁷

Multiple Choice

Simplify: $$\left(4y\right)^{-3}$$  

• $$\frac{1}{64y^3}$$  

• $$64y^{-3}$$  

• $$-12y^{-3}$$  

• $$\frac{64}{y^3}$$  

Multiple Choice

Simplify (2x⁴y⁷)³

• 6x⁷y¹⁰
• 6xy³²
• 8x¹²y²¹
• 8x⁷y¹⁰

Multiple Choice

(5³x²y⁴)⁰

• 5xy
• 1
• 0
• 5

Multiple Choice

Simplify: $$\left(2a^3b^4c^3\right)^2\cdot\left(4a^2bc^3\right)$$  

• $$16a^8b^9c^9$$  

• $$8a^8b^9c^9$$  

• $$8a^6b^5c^6$$  

• $$16a^5b^5c^6$$  

Multiple Choice

Simplify: $$\frac{\left(4x^2y^3\right)^0}{8x^3}$$  

• $$\frac{1}{8x^3}$$  

• $$\frac{y^3}{2x}$$  

• $$\frac{4y^3}{8x}$$  

• $$1$$  

Multiple Choice

Simplify: $$\frac{50r^6n^{-7}}{2n^2r^4}$$  

• $$25r^4n^5$$  

• $$\frac{25r^4}{n^5}$$  

• $$\frac{25r^2}{n^9}$$  

• $$25r^2n^{-9}$$