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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let ite be `f(x)=x+1/4` and `F(x)=4x^4+x^3-4x+1`
The easier system is to rewrite :
Let you see there is a rest `2!=0`
therefore `f(x)` doesn't divide`F(x)`
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`
Therefore, `x+1/4` is not a factor of F(x).` `
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