Answer:
[tex]P(x)=x^2-3x-28[/tex]
Last option
Step-by-step explanation:
Roots (Zeros) of Polynomials
A given polynomial P(x) is said to have a root or zero at x=a if P(a)=0.
We must find a polynomial which zeros are x=-4 and x=7. We can test each option, but let's derive the polynomial by multiplying the factors (x+4)(x-7)
[tex](x+4)(x-7)=x^2-7x+4x-28=x^2-3x-28[/tex]
So if our polynomial was
[tex]P(x)=x^2-3x-28[/tex]
its zeros will be x=-4 and x=7
Testing x=-4
[tex]P(x)=(-4)^2-3(-4)-28=16+12-28=0[/tex]
Testing x=7
[tex]P(x)=7^2-3(7)-28=49-21-28=0[/tex]
