Answer:
Factored form is
f(x)= (x-1)(x-3+√(-5))(x-3-√(-5))
Step-by-step explanation:
Given that
f(x)=x3−7x2+2x+4
To solve for x we factorise the right side
f(x)=x3−7x2+2x+4
Let us substitute x for various values to check whether remainder is zero.
i.e. f(1) = 1-7+2+4 =0
Hence x-1 is a factor
Do synthetic division to find the quotient
1 1 -7 2 4
1 -6 -4
----------------------
1 -6 -4 0
i.e. we get remainder 0 and quotient as
x^2-6x-4
Use completion of squares method to solve this
x^2-6x-4
= (x-3)^2+5=0
x-3= ±√(-5)
Or x=1,3+√(-5,) 3-√(-5,)
Are the roots
Factored form is
f(x)= (x-1)(x-3+√(-5))(x-3-√(-5))
