Answer:
the remainder is -49
Step-by-step explanation:
[tex]f(x) = 5x^3 + 7x + 5[/tex] is divided by [tex]x + 2[/tex]
To find out the remainder we use remainder theorem
Divisor is [tex]x + 2[/tex]. Set it =0 and solve for x
[tex]x+2=0 , x=-2[/tex]
Plug in -2 for x in f(x)
Replace all x by -2
[tex]f(x) = 5x^3 + 7x + 5[/tex]
[tex]f(-2) = 5(-2)^3 + 7(-2) + 5=-49[/tex]
So the remainder is -49
