Final Polynomial Lesson Review

Polynomial Arithmetic
Review

Moving on to something new tomorrow!

The largest exponent is the degree of a polynomial.

Degree

Fill in the Blanks

What is the degree?

4x⁴ + 5x - 2x⁸

Fill in the Blanks

What is the degree?

12x³ - 5x⁵ + 10x

This has 2 steps.
1) Put in standard form (highest exponent in front).
2) Combine like terms by the math is wants (add or subtract)

​

Add or Subtract

Match

Match the answer to the correct problem!

• (2x³+5x+2)+(4x³+x+5)

• (3x²+2x+1)+(2x²+3x+4)

• (x⁴+2x²+3)+(3x⁴+x²+1)

6x³ + 6x + 7

5x² + 5x + 5

4x⁴ + 3x² + 4

• 6x³ + 6x + 7

• 5x² + 5x + 5

• 4x⁴ + 3x² + 4

Match

Match the answer to the correct problem.

• (6x⁵+3x+9) - (x⁵+2x+1)

• (4x³+2x+5) - (2x³+x+3)

• (5x⁴+7x+2) - (3x⁴+2x+1)

5x⁵ + x + 8

2x³ + x + 2

2x⁴ + 5x + 1

• 5x⁵ + x + 8

• 2x³ + x + 2

• 2x⁴ + 5x + 1

2 Steps:
1) Multiply the big numbers.
2) Add the exponents for matching letters. (Or just bring the letter with you if there isn't one).

​

Multiply

Dropdown

2x(3x³ - 5x + 4) = ​

Select answer

Dropdown

(2x + 3)(x - 4) = ​

Select answer

​

3 Steps:
1) Put into a fraction.
2) The top numbers divided by the bottom number.
3) Subtract the exponent for matching letters.

Divide

Dropdown

(25x² - 15x) ÷ (5x) = ​

Select answer

Dropdown

(4x⁴ + 8x³ + 6) ÷ (2x) =​ ​

Select answer

Now you will practice a bit!

Multiple Choice

Add the polynomials.
(x + 5) + (2x + 7)

• 3x + 12
• 2x² + 35
• 2x² + 12x + 35
• 3x + 57

Multiple Choice

Add the polynomials.
(4x + 2) + (3x - 8)

• 7x - 6
• 12x - 16
• 12x + 16
• 12x² - 26x - 16

Multiple Choice

Subtract the polynomials.
(8x + 5) - (4x + 3)

• 4x + 2
• -4x - 15
• 32x² + 44x + 15
• 4x + 15

Multiple Choice

Subtract the polynomials.
(2x + 12) - (5x - 8)

• -3x + 20
• -3x + 4
• 7x + 4
• 10x² + 76x - 96

Multiple Choice

Multiply:
5x (3x² + 2x - 7)

• 15x³ + 10x² - 35x
• 60x³
• 8x³ + 7x² - 12x
• 15x² + 10x - 35x

Multiple Choice

Multiply:
-4 (3x² - 5x - 10)

• -12x² + 20x + 40
• 72x²
• -1x² + 20x - 40
• -12x² - 20x - 40

Multiple Choice

Divide the polynomial by the monomial.

• 15x⁹ - 8x³
• 3x⁶ - 8x³
• -5x¹²
• 3x⁶ - 40x³

Multiple Choice

Divide the polynomial by the monomial.

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

Multiple Choice

$$\frac{18y^{6\ }+9y^{4\ }-12y^2}{3y^2}$$  

• $$6y^2\ +3y^2\ -4y^2$$  

• $$15y^{4\ }+6y^2\ -\ 9$$  

• $$6y^{4\ }+3y^2-4$$  

• $$6y^{3\ }-3y^2\ +4y$$  

Multiple Choice

$$\frac{-12a^{4\ }+\ 6a^3}{6a^3}$$  

• $$2a$$  

• $$-2a+1$$  

• $$2a\ +1$$  

• $$-2a\ +\ 1a$$