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What must be added to 2x^4-5x^3+2x^2-x-3 so that the result is

Question

What must be added to $2 x^{4} - 5 x^{3} + 2 x^{2} - x - 3$ so that the result is exactly divisible by $(x - 2)$ ?

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Olivia Discussed

What must be added to

2 x^{4} - 5 x^{3} + 2 x^{2} - x - 3

so that the result is exactly divisible by

(x - 2)

9 mins ago

Discuss this question LIVE

9 mins ago

Text solutionVerified

Let the required number to be added be

k

. Then ,

p (x) = 2 x^{4} = 5 x^{3} + 2 x^{2} - x - 3 + k

and

g (x) = (x - 2) .

Now ,

g (x) = 0

x - 2 = 0

x = 2.

p (2) = 0

(32 - 40 + 8 - 5 + k) = 0

k = 5

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Question Text	What must be added to $2 x^{4} - 5 x^{3} + 2 x^{2} - x - 3$ so that the result is exactly divisible by $(x - 2)$ ?
Answer Type	Text solution:1
Upvotes	150