Answer:
The solved given equation is [tex]x^3+x^2+16x-20=(x-2)(x-2)(x+5)[/tex].
Step-by-step explanation:
Given equation is [tex]-3x^3-x^2+54x-40=2x^2+6x+20[/tex]
To solve the given equation:
[tex]-3x^3-x^2+54x-40-2x^2-6x-20=0[/tex]
[tex]-3x^3-3x^2+48x-60=0[/tex]
Multiply the above equation into [tex]-\frac{1}{3}[/tex] on both sides
[tex]-3x^3-3x^2+48x-60\times (-\frac{1}{3})=0\times (-\frac{1}{3})[/tex]
[tex]x^3+x^2+16x-20=0[/tex]
To sove the equation by using synthetic division method
2_| 1 1 -16 20
0 2 6 -20
___________
1 3 -10 0
Therefore x-2 is a factor
Therefore the quadratic equation is [tex]x^2+3x-10=0[/tex]
(x-2)(x+5)=0
(x-2)=0 or (x+5)=0
[tex]x^2+3x-10=(x-2)(x+5)[/tex]
Therefore the factors are x-2,x-2,x+5
Therefore the solved given equation is [tex]x^3+x^2+16x-20=(x-2)(x-2)(x+5)[/tex]
