roots of polynomial

Question

if x = -1 is a root of x³ + 4x² - x - 4 = 0, use synthetic division to factor polynomial completely, and list all real solutions of equation

Answer 1

if x = -1 is a root that means that (x+1) is a factor use that with synthetic division to simplify.

Look in to your book or Youtube to learn how to do synthetic division

_____________

-1 | 1 4 -1 -4

___ -1__-3__ 4___

1 3 -4 0

x² +3x -4

You can factor the above equation with normal methods

your answer should look like this Factors (x+1) (x ) (x ); x = -1,__, __

with the blanks filled in.

Answer 2

For synthetic division, put the root, x = -1 in the box and write out the coefficients of each of the terms beside it. Bring down the first coefficient, 1. Multiply that 1 with the number in the box, -1. Put that number under the 4. Add. Repeat those steps. The last number should be a zero. Since x = -1 is a root, that means x+1 is a factor. Factors divide evenly with no remainders.

-1| 1 4 -1 -4

__-1 -3 4_

1 3 -4 |0

The numbers under the line of synthetic division are the coefficients of the quotient polynomial:

x² + 3x -4 = 0

Factor:

(x + 4)(x - 1) = 0

x = -4; x = 1

All three roots are: x = -1, x = 1, and x = -4.