Factoring A Polynomial...2

[nycmathguy]

Section 2.3
Question 63

Part (a) Verify the given factors.

If x + 2 = 0, then x = -2.

Using synthetic division, I got the following resulting coefficients: 2, -3, 1, with remainder 0.
The quotient turns out to be 2x^2 - 3x + 1.

If x - 1 = 0, then x = 1.

Using synthetic division, I got the following resulting coefficients: 2, 3, -2, with remainder 0.
The quotient turns out to be 2x^2 + 3x - 2.

Part (b) Find remaining factor(s).

To do so, divide as follows:

Remaining factor(s) = f(x)/(given factors).

Using long division, I found the remaining factor to be 2x - 1.

Part (c) Write complete factorization.

(2x - 1)(x + 2)(x - 1)

Part (d) List all zeros.

If 2x - 1 = 0, then x = 1/2 is a zero.

If x + 2 = 0, then x = -2 is a zero.

If x - 1 = 0, then x = 1 is a zero.

Part (e) below.

 

[MathLover1]

perfect!

 

[nycmathguy]

perfect!

Ok. Problems with different parts take a long time to solve. I have notes should I desire to do a few more.