# Math Help - Factoring polynomial degree 4

1. ## Factoring polynomial degree 4

Show that x = -2.22 is a solution for:

2.00 x4 - 3.00x3 +5.00x = 70.0

When using a calculator I get 70.3. I have been unable to factor the equation so I’m wondering is this a solution obtained by a graph or is there a factoring method that will lead to this solution?

2. Originally Posted by wrjones
Show that x = -2.22 is a solution for:

2.00 x4 - 3.00x3 +5.00x = 70.0

When using a calculator I get 70.3. I have been unable to factor the equation so I’m wondering is this a solution obtained by a graph or is there a factoring method that will lead to this solution?
If the question is simply to show that x = -2.22 is a factor, then I suggest you use long/synthetic division to show that (x+2.22) divides into $2x^4 -3x^3 + 5x - 70$ without a remainder!

3. ## factor

Thanks for looking at the problem. It seems that by the fact I'm off by a half percent when just plugging in the number that there would be a remainder but I guess I will give it a try.

Thanks for looking at the problem.

4. You are completely right. x= -2.22 does NOT satisfy that equation.

5. Originally Posted by HallsofIvy
You are completely right. x= -2.22 does NOT satisfy that equation.
No, but the solutions to the equations are irrational, and the result x = -2.22 is a rounded effort.

The remainder is small enough to be neglected for all intents and purposes, imo.

6. Originally Posted by wrjones
Show that x = -2.22 is a solution for:

2.00 x4 - 3.00x3 +5.00x = 70.0

When using a calculator I get 70.3. I have been unable to factor the equation so I’m wondering is this a solution obtained by a graph or is there a factoring method that will lead to this solution?
As others said, the discrepancy is due to rounding.

None of the roots are rational, and although I was able to get an exact solution with CAS software, it was several pages' worth of radicals and fractions, so I think a numerical approximation works best here.

7. Originally Posted by wrjones
Show that x = -2.22 is a solution for:

2.00 x4 - 3.00x3 +5.00x = 70.0

When using a calculator I get 70.3. I have been unable to factor the equation so I’m wondering is this a solution obtained by a graph or is there a factoring method that will lead to this solution?
Only if rounded to two decimal places is -2.22 a solution to this, but such precision is not acceptable unless the question asks for it, which may be the case as the coefficients are given to two decimal places.

CB