Question

USING FACTOR THEOREM, CHECK WHETHER THE POLYNOMIAL G(X) IS A FACTOR OF P(X) OR NOT, IN THE CASE :
P(X) = X CUBE - 2X SQUARE - 5X + 6 ; G(X) = X + 2​

Answer 1

Remainder Theorem :

__________....

g(x) = x + 2

→ x + 2 = 0

→ x = 0 - 2

.°. x = -2

p(x) = x³ - 2x² - 5x + 6

Putting the value of x

→ (-2)³ - 2(-2)² - 5(-2) + 6

→ -8 - 2(4) - (-10) + 6

→ -8 - 8 + 10 + 6

→ -16 + 16

→ 0

.°. So, g(x) is a factor of p(x) because the remainder is 0...

Answer 2

❱•❰

Given:-

p(X) = X³ - 2X² - 5X + 6

g(X) = X + 2

Zero of g(x):-

X + 2 = 0

→ X = - 2

Putting the value of X to p(X):-

p(X) = X³ - 2X² - 5X + 6

∴ p(- 2) = (- 2)³ - 2(- 2)² - 5(- 2) + 6

= - 8 - 2(4) + 10 + 6

= - 8 - 8 + 10 + 6

= - 8 - 8 + 16

= - 16 + 16

= 0

Since, the remainder is (0),

∴ g(X) is a factor of p(X).