SOLUTION: use the p over q method and synthetic division to factor the polynomial P(x). then solve P(x)=0 P(x)=x^3+4x^2+x-6

Question 1090305: use the p over q method and synthetic division to factor the polynomial P(x). then solve P(x)=0
P(x)=x^3+4x^2+x-6
Found 2 solutions by Boreal, MathLover1:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
P(x)=x^3+4x^2+x-6
p is 6 and q is 1, the coefficient of x^3
therefore the possible integer roots are +/-1,2,3,6
synthetic division with
1/1----4----1---minus 6
==1==5----6----0
1 is a root, so (x-1) is a factor
the other factor may be read off the division as x^2+5x+6, which is (x+3)(x+2)
Those are the three factors, and roots are -3, -2, and 1

Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
P(x)=x^3+4x^2+x-6

1. Arrange the polynomial in descending order:

2. Write down all the factors of the constant term. These are all the possible values of p .
, all the factors are
= ,� ,,
3. Write down all the factors of the leading coefficient. These are all the possible values of q .

4.Write down all the possible values of . Remember that since factors can be negative, and must both be included. Simplify each value and cross out any duplicates.
=�, �,�, �,... (eliminate , it is product of and )
=�, �,�,
5. Use synthetic division to determine the values of for which . These are all the rational roots of .
The synthetic division table is: if
|.... .... .... ......
....................... ...... ..
-----------------------------------------
................................-> reminder=> ,=> a root

The synthetic division table is: if
|.... .... .... ......
....................... .... ....
-----------------------------------------
...........................-> reminder => is root
The synthetic division table is: if
|.... .... .... ......
....................... ......
-----------------------------------------
................................-> reminder=> ,=> is a root

The synthetic division table is: if
|.... .... .... .. ....
................... .... .. ....
-----------------------------------------
......... ........ ....... ....... -> reminder=> ,=> a root

The synthetic division table is: if
|.... .... .... .. ....
................... .... .. ....
-----------------------------------------
......... ........ ....... ........ -> reminder=> ,=> is a root

The synthetic division table is: if
|.... .... .... ......
....................... ......
-----------------------------------------
................................-> reminder=> ,=> a root

then solve

if =>
if =>
if =>

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