Given a polynomial f(x), if (x + 5) is a factor, what else must be true?

f(0) = 5

f(0) = -5

f(5) = 0

f(-5) = 0

Question

Given a polynomial f(x), if (x + 5) is a factor, what else must be true?

f(0) = 5

f(0) = -5

f(5) = 0

f(-5) = 0

ganeshie8 · Answer

since (x+5) is a factor, u can write the original polynomial as :-
f(x) = (x+5)(something)
plugin x = -5
f(-5) = ?

mathmale · Answer

Brad:  As a general rule, if (x+a) is a factor of a given polynomial, then x=a is a root of the polynomial.  Can you use this fact to choose the correct answer?

anonymous · Answer

f(-5) = (-5 + 5)

mathmale · Answer

which equals what?

anonymous · Answer

attachment

anonymous · Answer

so the last option?

mathmale · Answer

Right, and if a function's value is 0 for some particular x value, that means that that x-value is a ???? of the function.

anonymous · Answer

0?

mathmale · Answer

think of a word, not a numerical value.

anonymous · Answer

is this when imaginary numbers are used?

mathmale · Answer

Not quite, but thanks for the proposal.  Here's what I was driving at:  If a function's value is zero at a particular x-value, that x-value is a root (or zero) of the function.

anonymous · Answer

I'm confused now lol