Find the Remainder (Without division), on dividing, x^3 - 3x^2 + 5x + 11x by (x+2)
Answers
Given :- Find the Remainder (Without division), on dividing, x^3 - 3x^2 + 5x + 11 by (x+2) ?
Solution :-
we know that, according to remainder theorem, when p(x) is divided by (x - a) , it gives remainder as p(a) .
so,
→ (x - a) = (x + 2)
→ a = (-2)
then,
→ p(x) = x³ - 3x² + 5x + 11
→ p(-2) = (-2)³ - 3(-2)² + 5(-2) + 11
→ p(-2) = (-8) - 3 * 4 - 10 + 11
→ p(-2) = (-8) - 12 - 10 + 11
→ p(-2) = (-8) - 22 + 11
→ p(-2) = (-30) + 11
→ p(-2) = (-19) (Ans.)
therefore, when (x³ + 3x² + 5x + 11) is divided by (x+2) , remainder will be (-19) .
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Given : x³ - 3x² + 5x + 11x
To Find : Remainder (Without division), on dividing by x + 2
Solution:
x³ - 3x² + 5x + 11x
First simplify the polynomial as it has like terms
x³ - 3x² + 16x
Let say P(x) =x³ - 3x² + 16x
As per remainder theorem if if polynomial P(x) divided by (x-a) then
remainder is P(a)
Here x + 2 = x - (-2)
Hence P(-2) will give remainder
P(x) = x³ - 3x² + 16x
=> P(-2) = (-2)³ - 3(-2)² + 16(-2)
=> P(-2) = -8 - 12 - 32
=> P(-2) = -52
Remainder is -52
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