1. (a) Given the following equation, X^4-6x^3-2x+7 use synthetic division to test the following 3 pts and show if they are a root or not. Must show synthetic division for all 3 of the following test pts. Test these 3 possible root pts also called possible zeros using synthetic division. (x,y) = (4, 0) ; ( -1, 0) ; (1, 0).'

2. Using the rational root theorem, list the possible zeros:

Using p/q list all the possible zeros of the following equation: 4x^2 – 6x - 5 = 0.

Hint: there are 8 correct answers.

Suggested format for answer:

List factors of p:

List factors of q:

List possible zeros: +/- p/q

May also use a punnet square to show 12 possible answers as shown in class (plus and minus each case makes 2 of the 12)

3. Simplify the expression (x^4+4x^3-9x-2) (x+2) using synthetic division. Show your work just an answer without showing the synthetic division will get a zero grade. After doing the synthetic division, which gives you just coefficients. Convert the coefficient quotient answer, into a polynomial with variable x and the correct exponent powers in it. Convert your coefficient answer into a polynomial.

Hint: remember to fill in any missing degree terms in your dividend with coefficients that are zero to represent missing place holders. Hint2 : Your final remainder is a zero. If you do not get a zero as a remainder, you are doing something wrong.

Guest Jan 22, 2022