Using remainder theorem, find the remainder when: f(x) = 3x^3 − 2x^2 − 5x + 6 is divided by (x + 2).

By remainder theorem, If f(x) is divided by (x - a), then remainder = f(a). Let f(x) = x3 - 2x2 - 5x + 6 Divisor : ⇒ x + 2 = 0 ⇒ x = -2 Substituting x = -2 in f(x), we get : ⇒ f(-2) = (-2)3 - 2(-2)2 - 5(-2) + 6 = (-8) - 2(4) - 5(-2) + 6 = -8 - 8 + 10 + 6 = 0. Hence, remainder = 0.

Mathematics

Using remainder theorem, find the remainder when:
f(x) = x³ - 2x² - 5x + 6 is divided by (x + 2).

Factorisation

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Answer

By remainder theorem,

If f(x) is divided by (x - a), then remainder = f(a).

Let f(x) = x³ - 2x² - 5x + 6

Divisor :

⇒ x + 2 = 0

⇒ x = -2

Substituting x = -2 in f(x), we get :

⇒ f(-2) = (-2)³ - 2(-2)² - 5(-2) + 6

= (-8) - 2(4) - 5(-2) + 6

= -8 - 8 + 10 + 6

= 0.

Hence, remainder = 0.

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Mathematics

Using remainder theorem, find the remainder when:
f(x) = x³ - 2x² - 5x + 6 is divided by (x + 2).

Factorisation

Answer

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Answer

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