Answer:
the factors of f(x)=x^3+8x^2+5x-50 are (x-2)(x+5)(x+5)
Step-by-step explanation:
We need to factorise the function [tex]f(x)=x^3+8x^2+5x-50[/tex]
If a number is a factor of this function than it must be completely divisible by last co-efficient. Our last co-efficient is -50
Checking few numbers:
[tex]f(1)=(1)^{3}+8(1)^2+5(1)-50\\f(1)=1+8+5-50\\f(1)=-32\\Now \ putting \ x= 2 \\f(2)=(2)^{3}+8(2)^2+5(2)-50\\f(2)=8+8(4)+10-50\\f(2)=8+32+10-50\\f(2)=0[/tex]
So, f(2)=0 which means x-2 is a factor of the given function. Now we will perform long division of [tex]x^3+8x^2+5x-50[/tex] by (x-2) to find other factors
The long division is shown in figure attached.
After long division we get: [tex]x^2+10x+25[/tex]
The equation [tex]x^2+10x+25[/tex] can be further simplified as: (x+5)(x+5) or (x+5)^2
So, the factors of f(x)=x^3+8x^2+5x-50 are (x-2)(x+5)(x+5)
