Answer:
4
Step-by-step explanation:
We are given a polynomial of degree 4 with five terms.
We have to find atmost number of different linear factors.
Let the polynomial of degree 4 with 5 terms
[tex]x^4+bx^3+cx^2+dx+e[/tex]
It can be written as the product of linear factors
[tex](px-u)(qx-v)(rx-w)(sx-y)[/tex]
We know that
Number of linear factors=Degree of polynomial
Consider , a quadratic polynomial
[tex]x^2+3x+2[/tex]
[tex](x+2)(x+1)[/tex]
Degree of polynomial=2
Number of linear factors=2
Degree of polynomial=Number of linear factors
Hence, the polynomial could have atmost different linear factors=4
