Linear Factors of a polynomial?

Question

Write the following polynomial in terms of its linear factors:

P(x)=x^4-5x^3+2x^2+22x-22


So far I have used synthetic division and found that there are two zeros and the upper boundry is 5 while the lower is -2. I honestly am not even sure if I am even on the right path. Can someone please help me?

Thank you!

Answer 1

This polynomial doesn't have any rational zeros at all. (If there were, they would have to be ±1, ±2 or ±11 and none of these work.)

However, I think you may have mistyped it, since there are two nice integers where the value is -2. If you actually meant
P(x)=x^4 - 5x^3 + 2x^2 + 22x - 20
then we get P(1) = P(-2) = 0 and so
P(x) = (x-1) (x^3 - 4x^2 - 2x + 20)
= (x-1) (x+2) (x^2 - 6x + 10)
= (x-1) (x+2) ((x-3)^2 + 1)
= (x-1) (x+2) (x-3+i) (x-3-i).

Answer 2

Okay so you've found two zeros, so you should now have a quadratic equation.Find zeros with the quadratic formula, and then write it in the form:

(x - a)(x - b)(x - c)(x - d)

Where a,b,c, and d are the signed values of each of your zeros.
These are the linear factors.

Answer 3

What you solved and what the respond in the e book are the two comparable. you may desire to change your answer as follows to get the e book answer. P(x) = 2x(x+a million)(x-3/2)x-2) is your answer. Take the main appropriate coefficient 2 and multiply with the 2d bracket. The e book answer follows.