Polynomials 4/3&4

Polynomials

Adding & Subtracting

#1 Rule

​Combine LIKE terms.

Match

Match the like terms

• 5x

• -2y

• 16xy

• 4x²

• 3

-25x

5y

-3xy

9x²

-2

• -25x

• 5y

• -3xy

• 9x²

• -2

Flip everything to the right!

​Subtraction Signs

Change NOTHING

Addition Signs

Replace this with a header

​(3-2x+2x²)+(4x-5+3x²)

​(4x-2x³)+(5x³-4x+5)

Adding

OR YOU CAN GRAPH IT ON DESMOS

ONLY if there is ONE letter

Multiple Choice

Simplify the expression.

(4a³ - 8a - 4a²) + (7a³ - 7 - 6a)

• 11a³ - 4a² - 14a - 7

• 5a³ - 4a² - 14a - 7

• 5a³ - 4a² - 20a - 7

• 5a³ - 9a² - 20a - 7

(4n²-8n+4)-(8n²+4n⁴+1)

(3-2x+2x²)-(4x-5+3x²)

Subtracting

OR YOU CAN GRAPH IT ON DESMOS

ONLY if there is ONE letter

Multiple Choice

Subtract: (2a² + 5a + 3) -(a² - 3a - 4)

• 3a² + 2a - 1
• a² + 8a + 7
• 3a² + 8a + 7
• a² + 2a - 1

Multiplying

(x+5)(x+4)

BOX FOIL

Multiplying

(4x+1)(5x-2)

BOX FOIL

OR YOU CAN GRAPH IT ON DESMOS

ONLY if there is ONE letter

Multiple Choice

Multiply the binomials

(2x - 1)(x + 2)

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

Factoring

GRAPH them on DESMOS

The equation or expression in the question goes on line 1.

The answer choices go on lines 2, 3, and 4.

Change all letters to X.

Multiple Choice

Factor completely:
 3x² + 5x - 12

• (3x + 4)(x-3)
• (3x - 4)(x + 3)
• (3x + 3)(x -4)
• (3x - 3)(x + 4)

Multiple Choice

Factor completely:

4x² - 64y²

• I'm too lazy to type it in desmos.

• ( 2x - 32y) (2 x + 32y) 
• ( 2x - 8y) (2 x - 8y) 
• ( 2x - 8y) (2 x + 8y) 

What do the factors mean?

Factors are just lines that go through the x-intercepts of the quadratice function.

​Factors will cross on the x-intercepts

Multiple Choice

Which line represents a factor of the quadratic function?

• The blue line

• The green line

• The purple line

• The black line

Multiple Choice

Which expression is a factor of $$30x^2-4x-16$$

• $$5x+4$$

• $$3x-2$$

• $$5x-4$$

• $$3x-4$$

Multiple Choice

Which expression is a factor of $$10x^2-19x+6$$

• $$10x-3$$

• $$10x-1$$

• $$5x-3$$

• $$5x-2$$