Dividing Polynomials

Dividing Polynomials

Multiple Choice

Find the product:

(3x + 2)(2x + 4)

• 6x² + 16x + 8

• 5x² +11x + 6

• 5x² + 16x + 6

• 6x² + 11x + 8

Multiple Choice

Evaluate the expression using the quotient rule.

• x¹³
• x⁵
• x³⁶
• x^-5

Multiple Choice

• 1/m²
• m²
• m⁸
• 1/m⁸

Multiple Choice

• 5w ² − 4w + 3
• 12w ² − 9w + 6
• 12w ² − 12w + 9
• 5w ² − 12w+ 9

Multiple Choice

• 4y⁶
• 4y²²
• 30y⁶
• 30y²²

Multiple Choice

• 5p² - 16p
• 5p + 4
• 5p - 4
• 5p + 4p

Dividing Polynomials with Long Division

by Tanner Howell

​This is a separate example for you to view. Notice that the remainder is written a bit differently in this problem.

Multiple Choice

Divide:

(4x² - 24x + 35) / (2x - 5)

• 2x - 7

• 2x - 12

• 2x + 12

• 2x + 7

Multiple Choice

Find the quotient using long division

• $$4x-2$$

• $$4x+2$$

• $$4x-2+\frac{1}{3x-1}$$

• $$4x+2+\frac{1}{3x-1}$$

Open Ended

Nancy Pi is a YouTube favorite of mine, so let's see how she approaches synthetic division. What do you think about Nancy Pi? If you like her explanations, follow her on YouTube.

What is synthetic division?

• Shortcut way to divide polynomials

• Uses the roots (not factor form) as the divisor

• Uses the coefficients of the terms, and not the variables, as the dividend

Steps to dividing by synthetic division

• 1. Change the factor form of the divisor to the root. (factor form is (x - 3), root is 3)

• 2. Write out the polynomial to be divided in descending form, writing in zeros for the terms that are missing. For example: x⁴ + 2x² + 4 would be written as: x⁴ + 0x³ + 2x² + 0x + 4

Steps to dividing by synthetic division (cont)

• 3. Write out the coefficients only of the polynomial, including signs and including the 0's

• 4. Write the root to the left of the coefficients with a vertical bar between it and the coefficients and a horizontal line underneath the coefficients (like an upside-down division symbol)

Steps to dividing by synthetic division (cont)

• 5. Bring the first coefficient down below the line, without doing anything to it

• 6. Multiply the coefficient by the root, and add the number to the next term.

• 7. Multiply the sum by the coefficient and add to the next term.

Multiple Choice

x³-3x²-10x+24 ÷ x+3

• x²-7x+5
• x-8
• x²-6x+8
• x+9

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

(2x³ + 5x² + 9) ÷ (x + 3)

• 2x² - x + 3

• 2x³ - x² + 3x

• 2x² + 11x + 33 + 108/x+3

• 2x² - 5x + 12