a) Not a factor
b) Not a factor
1) To check whether those given polynomials are factors of f(x), we need to remind of the definition of the factor theorem:
2) So, let's begin with p+2
[tex]\begin{gathered} p+2=0 \\ p=-2 \\ f(2)=(2)^4+6\cdot(2)^3+11(2)^2+29(2)-13 \\ f(2)=16+48+44+58-13 \\ f(2)=153 \end{gathered}[/tex]
Since f(2) is not equal to zero then (p+2) is not a factor
b)p+5
Similarly, we can write out the following:
[tex]\begin{gathered} p+5=0\rightarrow p=-5 \\ f(-5)=(-5)^4+6(-5)^3+11(-5)^2+29(-5)-13 \\ f(-5)=625-750+275+29\left(-5\right)-13 \\ f(-5)=625-750+275-145-13 \\ f(-5)=-8 \end{gathered}[/tex]
As we can see, p+5 is also not a factor of f(x), in other words, -5 is not a root as well as 2 of this polynomial.
