M3 - Polynomial Operations Review

M3 - Polynomial Operations Review

Multiplying, Factoring, Dividing

Skills from Math 1 and Math 2

• Multiplying

• Factoring

Multiplying

Distribute or use the Box Method to help you organize all the steps

Multiple Choice

6v(2v + 3)

• 12v+18

• 15v² + 8v

• 12v² + 18v

• 12v² + 18v²

Multiple Choice

(x − 3)(6x − 2)

• 6x² − 20x + 6

• 6x² + 20x - 6

• 6x² +6

• 6x + 6

Multiple Choice

(4a + 2)(6a² − a + 2)

• 24a³ + 16a² + 6a + 4

• 24a³ + 8a² + 10a + 4

• 24a³ + 8a² + 6a + 4

• 24a³ - 8a² - 6a + 4

Factoring

• GCF

• Difference of Squares

• Unfoiling (aka Trinomial factoring)

• Slide-n-Divide

Multi-Step Factoring

• Check for GCF FIRST

• After GCF, what pattern does it exhibit?

• This one is a difference of squares, hence the result

Factor with imaginary Difference of Squares

We will learn about how imaginary solutions come in pairs. They are equal and opposite. This is essentially a pattern similar to the difference of squares. Observe in the picture at right:

Multiple Choice

Multiply and Simplify:

(x + 2i)(x - 2i)

• x² - 4

• x² - 4i²

• x² + 4

• x² - 4i + 4

Multiple Choice

k² -36

• (k+6)(k-6)

• (k-6)²

• (k+6)²

• (k+6)²(k-6)²

Multiple Choice

Factor x² + 7x + 12

• (x + 2)(x + 10)
• (x + 3)(x + 4)
• (x + 4)(x + 5)
• (x + 4)(x + 6)

Multiple Choice

 $x^2+64$  

Factor the expression:

• (x + 8)(x + 8)

• (x - 8)(x - 8)

• (x - 8)(x + 8)

• (x - 8i)(x + 8i)

Multiple Choice

• 4x

• 21

• 2x-1

• 10x

Multiple Choice

For synthetic division, what would be the divisor (outside the box)?

• -1
• -2
• 2
• 1

Multiple Choice

What should be the order of the polynomial coefficients if

(3x - 4x³+ 6x⁴ + 1) / (x + 3)

• 3 0 -4 6 1

• 6 -4 3 1 0

• 6 -4 0 3 1

• -6 4 0 -3 -1

Multiple Choice

Divide.

• (x + 4)/(x + 3)
• x + 5
• x + 4  R 5
• x + 4 R -5

Multiple Choice

(3x³ + 5x - 1) ÷
(x + 1)

• 3x³ - 3x² + 8x - 9
• 3x² - 3x + 8 - (9/x+1)
• 3x² + 3x + 8 + (7/x+1)
• 3x³ + 3x² + 8x + 7

Multiple Choice

What is the remainder of  (3x³ -5x² -4x +1) ÷ (x + 3)?

• -25
• 25
• 113
• -113