Answer:
B.X+2
Step-by-step explanation:
-2^3+12X-2^2+9X-2-22
-8+48-18-22
40-40=0
The following is a factor of the polynomial is x+2.
Factor theorem is a special kind of the polynomial remainder theorem that links the factors of a polynomial and its zeros.
The factor theorem removes all the known zeros from a given polynomial equation and leaves all the unknown zeros. The resultant polynomial has a lower degree in which the zeros can be easily found.
As per the factor theorem, (y – a) can be considered as a factor of the polynomial g(y) of degree n ≥ 1, if and only if g(a) = 0. Here, a is any real number. The formula of the factor theorem is g(y) = (y – a) q(y). It is important to note that all the following statements apply for any polynomial g(y):
Given:
f(x)=x³ + 12x² + 9x - 22
To the above equation (x + 2) is a factor of x³ + 12x² + 9x - 22.
As,
f(-2)= (-2)³ + 12(-2)² + 9(-2) - 22
f(x)= -8 + 48 -18 -22
f(x)= 40 -40
f(x) = 0
Hence, the factor of x+2
Learn more about factor theorem here:
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