When the polynomial in P (x) is divided by (x + a), the remainder equals P (a)

This is a false statement:

Step-by-step explanation:

According to Remainder Theorem dividing the polynomial by some linear factor x + a, where a is just some number. As a result of the long polynomial division, you end up with some polynomial answer q (x) (the "q" standing for "the quotient polynomial") and some polynomial remainder r (x).

P (x) = (x+/-a) q (x) + r (x)

P (x) = (x+a) q (x) + r (x). Note that for x=-a

P (-a) = (-a+a) q (-a) + r (-a) = 0 * q (-a) + r (-a)

P (-a) = r (-a)

It means that P (-a) is the remainder not P (a)

Thus the given statement is false ...