The Factor Theorem

6 = 3 × 2

6÷2 => remainder = 0

6÷3 => remainder = 0

အၾကြင္း 0 ရေအာင္စားႏိုင္ေသာ စားကိန္းကို တည္ကိန္း၏ factor ဟုေခၚသည္။

The Factor Theorem:

Let f(x) be a polynomial. Then (x-k) is a factor of f(x) if and only if f(k) = 0.

Example 1

Find what value p must have in order that x – p may be a factor of
4x³ – (3p + 2)x² – (p² – 1)x + 3.

Let f(x) = 4x³ – (3p + 2)x² – (p² – 1)x + 3.
x – p is a factor of f(x) only if
f(p) = 0
4p³ – (3p + 2)p² – (p² – 1)p + 3 = 0
2p² – p – 3 = 0
(p + 1) (2p – 3) = 0
p = -1 or p = 3/2