Ques.no. 16 solve with explanation...
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Note: When f(x) is divided by g(x) the remainder should be 0. If it not zero, then we have to subtract the remainder from f(x) so that it is divisible by g(x).
Now,
Given, f(x) = 8x^4 + 14x^3 - 2x^2 + 7x - 8.
Given, g(x) = 4x^2 + 3x - 2.
We have to divide f(x) by g(x).
4x^2 + 3x + 2) 8x^4 + 14x^3 - 2x^2 + 7x - 8 ( 2x^2 + 2x - 1
8x^4 + 6x^3 - 4x^2
-----------------------------------------------
8x^3 + 2x^2 + 7x - 8
8x^3 + 6x^2 - 4x
--------------------------------------------------
4x^2 + 11x - 8
4x^2 - 3x + 2
------------------------------------------------------
14x - 10
We get the remainder = 14x - 10.
Hence, 14x - 10 should be subtracted to 8x^4 - 14x^3 - 2x^2 + 7x - 8 So that it can be divisible by 4x^2 + 3x - 2.
The answer is 14x - 10 ----- Option (C).
Verification:
We know that Dividend = Divisior * Quotient + Remainder
⇒ (2x^2 + 2x - 1) * (4x^2 + 3x - 2) + (14x - 10)
⇒ 8x^4 + 14x^3 - 2x^2 - 7x + 2 + 14x - 10
⇒ 8x^4 + 14x^3 - 2x^2 + 7x - 8
⇒ Dividend.
Hope it helps!