Divide using synthetic division (2x^4 + 6x^3 + 5x -6) ÷ (x + 2)?

Question

a. 2x^3 + 2x² - 4x +13 - 32/(x+ 2)

b 2x² + 2x + x - 8

c 2x² + 2x +x - 8/(x + 2)

2. (6x^3 - 16x² + 11x - 5 ÷ (3x - 2)

a 6x² - 12x + 3 - 9/(3x -2)

b 2x² - 4x + 1 - 3/(3x - 2)

c 2x² - 4x + 1 - 1/(3x - 2)

I am so confused please help me

Answer 1

synthetic division is a weird method, hopefully they explain in your book as its not something that can easily be shown in a text box. First your divisor is the value when x + 2 = 0, so x = -2

so your going to be dividing by a form of x so your answer will be something like

Ax^3 + Bx^2 + Cx + D and we need to find the coefficients

so A = the first number of your polynomial, so we will have

2x^3 + Bx^2 + Cx + D

then our B is going to be the next term, which is 6, plus our A term times our divisor

so 6 + (2*-2) = 6 + (-4) = 2, which will be our B term, so we have

2x^3 + 2x^2 + Cx + D

then our C is going to be the next term, which is 5, plus our B term times our divisor

so 5 + (2*-2) = 5 + (-4) = 1, which will be our C term, so we have

2x^3 + 2x^2 + x + D

then our D is going to be the next term, which is -6, plus our C term times our divisor

so -6 + (1*-2) = -6 + (-2) = -8, which will be our D term, so we have

SOLUTION: 2x^3 + 2x^2 + x - 8

Here's a visual representation of what we are doing:

http://www.wtamu.edu/academic/anns/mps/m...

Answer 2

answer to number 1 is A

answer to number 2 is A [i'm almost sure, you might want to do it yourself just to check]

this website explains how to get those answers

http://www.purplemath.com/modules/synthd...