synthetic division

[marshall1432]

1. Can synthetic division be used to divide 2x2 + x - 1 by x2 - 1? Answer yes or no and briefly explain why you selected the answer you did.

no. it cannot divide all the way through

2. Use synthetic division to find the quotient and remainder when f(x) = 3x4 + 8x2 - 7x + 4 is divided by x - 1.

3x3+3x2-5x2+7x+3

3. Use synthetic division to find the quotient and remainder when f(x) = x3 + 4x2 - 3x + 1 is divided by x - 1/2.

x2-8x-3

4. Use synthetic division to determine whether x + 1 is a factor of 2x3 - 3x2 + 1. (Answer either "Yes, it is." or "No, it's not.")

yes

5. Given that x = -2 is a zero of f (x) = 2x3 + 3x2 - 5x - 6, use synthetic division to completely factor f.

i dont know how to factor this.

 

[tkhunny]

1) What is the definition of "Synthetic Division"? Is the divisor NECESSARILY from a linear factor? In any case, for x^2 - 1, you can factor it (x+1)(x-1) and use the linear Synthetic Division twice. Does that qualify? There is a way to do it with a quadratic divisor, but it is tedious.

5) Do you know that the numbers along the bottom of the tableau give you the coefficients of the new "reduced" factor?

x = -2 is a zero of f (x) = 2x3 + 3x2 - 5x - 6

You are told that (x+2) is a factor. The bottom row of a Synthetic Division gives:

2 -1 -3 0

This means 2x^3 + 3x^2 - 5x - 6 = (x+2)(2x^2 - x - 3)

 

[marshall1432]

What is the definition of "Synthetic Division"? Is the divisor NECESSARILY from a linear factor? In any case, for x^2 - 1, you can factor it (x+1)(x-1) and use the linear Synthetic Division twice. Does that qualify? There is a way to do it with a quadratic divisor, but it is tedious.

Do you know that the numbers along the bottom of the tableau give you the coefficients of the new "reduced" factor?

x = -2 is a zero of f (x) = 2x3 + 3x2 - 5x - 6

You are told that (x+2) is a factor. The bottom row of a Synthetic Division gives:

2 -1 -3 0

This means 2x^3 + 3x^2 - 5x - 6 = (x+2)(2x^2 - x - 3)

sorry, not following.

 

[stapel]

sorry, not following.

What do you mean, "not following"? These are conceptual exercises, and the tutor asked the leading questions which should have led you immediately to the answers.

1) Has your class not yet studied synthetic division? Has this process not yet been defined? (The answer follows immediately from the definition, which is why the tutor suggested that you review it.)

2) No. Unfortunately, since you have again not shown your work, I'm afraid it is not possible to help you find your error. Sorry.

3) No. Unfortunately, since you have again not shown your work, I'm afraid it is not possible to help you find your error. Sorry.

4) Is your answer a guess?

5) The tutor's reply explained the reasoning and methodology behind using synthetic division to factor polynomials. Since this seems not to be familiar to you, it would probably be wise to hire a tutor and sit down with him for a few hours to re-learn the basic concepts behind this process. (As has been explained previously, we cannot provide the necessary instruction within this environment.)

My best wishes to you.

Eliz.