Solving a Polynomial Equation | jensenmath.ca #maths #math #advancedfunctions

[carultch]

There's two other solutions as well:
x = -1/4 + 1/4*sqrt(3)*i
x = -1/4 - 1/4*sqrt(3)*i

[Nxbulah_]

8x^3(x+2)1(x+2) -> (8x³+1)(x+2) -> FOIL -> 8x⁴+16x³+x+2. Then 8x³+1=0 and x+2=0. X=-2 and 8³=1. 1 to the cube root is like 1 so yoyr answer is {-2, 1} I think

[imcalculus]

Using remainder theorem, this question can be solved faster if u can do polynomial division faster than factorisation

[ParadiseofDarkness]

I'm legally to autistic for this.

[ChavoMysterio]

8x⁴+16x³+x+2=0
8x³(x+2)+1(x+2)=0
(8x³+1)(x+2)=0

8x³+1=0
(2x)³+1³=0
(2x+1)(4x²-2x+1)=0

4x²-2x+1=0
16x²-8x+4=0
16x²-8x+1=-3
(4x-1)²=-3
|4x-1|=i√3
4x-1=±i√3
4x=1±i√3
x=¼(1±i√3) ❤❤

2x+1=0
2x=-1
x=-½ ❤

x+2=0
x=-2 ❤