If P(x) is a polynomial in x for which P(3)=0, then..?
a) x-3 is a factor of P(x)
b) x+3 is a factor of P(x)
c) 3x is a factor of P(x)
d) x^3 is a factor of P(x)
The Remainder Theorem shows that (a) is the answer.
To determine the correct answer, let's break it down step by step:
Since we are given that P(3) = 0, this means that when we substitute x = 3 into the polynomial P(x), we get a zero result. Mathematically, it can be written as P(3) = 0.
Now, suppose x - a is a factor of the polynomial P(x), where "a" is some constant. In this case, if we substitute x = a into P(x), we would get P(a) = 0. This is due to the fact that when x equals a, one of the factors is equal to zero, making the whole polynomial zero.
Comparing the given information P(3) = 0 with the concept we just discussed, we can conclude that (a) x - 3 is a factor of P(x) must be the correct answer.