Answer:
The given polynomial f(x) can be factorized as [tex](x^3+4x-5) = (x-1) \times (x +5)[/tex]
Step-by-step explanation:
Here, the given function is: [tex]f(x)=x^3+4x-5[/tex]
Now If we try and put any arbitrary value say x = 1, we get
[tex]f(1)=(1)^3+4(1)-5 = 5- 5 = 0[/tex] , or f(1) = 0
⇒ x =1 is the zero of the given polynomial.
⇒ (x-1) is the ROOT of the Polynomial.
Now, dividing the polynomial, with this root, we get:
[tex]\frac{x^3+4x-5}{(x-1)} = (x +5)\\\implies (x^3+4x-5) = (x-1) \times (x +5)[/tex]
⇒ (x+5) is the another ROOT of the Polynomial.
So, the given polynomial p(x) has two zeroes 1 and -5.
Hence, the given polynomial f(x) can be factorized as [tex](x^3+4x-5) = (x-1) \times (x +5)[/tex]
