# PLEASE HELP ME SOLVE THIS. USE SYNTHETIC DIVISION TO DETERMINE WHETHER X + 1/4 IS A FACTOR OF F(X)= 4X^4 + X^3 -4X +1. I DONT THINK I CAN USE FRACTION ON SYNTHETIC DIVISION. 4X +1 DIVIDED BY THE...

PLEASE HELP ME SOLVE THIS. USE SYNTHETIC DIVISION TO DETERMINE

WHETHER X + 1/4 IS A FACTOR OF F(X)= 4X^4 + X^3 -4X +1.

I DONT THINK I CAN USE FRACTION ON SYNTHETIC DIVISION.

4X +1 DIVIDED BY THE F(X) ONLY ON LONG DIVISION ??????

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### 2 Answers

Let `x +1/4 = 0`

and F(x) = 0.

From `x + 1/4 = 0` , solve for x.``

Subtract 1/4 to both sides.

`x+1/4 - 1/4 = 0-1/4`

`x = -1/4`

Now that you have a value for x, substitute that in `4x^4 + x^3 -4x +1`

Since to get the roots of an expression, you let that expression equal to 0. We are assuming that x+1/4 is a factor, so -1/4 is a root. So to check if it is a factor, it must satisfy F(x) = 0. In other words, the left side and right side of the equation must be 0 if you plug-in -1/4 into the expression. So,

`0 =? 4(-1/4)^4 + (-1/4)^3 - 4(-1/4) + 1`

`0!= 2`

Therefore, `x+1/4` is not a factor of F(x).` `

let ite be `f(x)=x+1/4` and `F(x)=4x^4+x^3-4x+1`

The easier system is to rewrite :

`F(x)=x^3(4x+1) -4x+1=x^3(4x+1)-(4x+1)+2=`

`(x^3-1)(4x+1)+2`

Let you see there is a rest `2!=0`

therefore `f(x)` doesn't divide`F(x)`