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Question

Using long division method, divide the polynomial x416x by x+2

A
x32x2+4x8
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B
x3+2x2+4x8
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C
x32x24x8
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D
x32x2+4x+8
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Solution

The correct option is A x32x2+4x8
Let us first factorize x416 as shown below:

x416=(x2)242=(x2+4)(x24)(a2b2=(a+b)(ab))=(x2+4)(x222)=(x2+4)(x+2)(x2).....(1)

Now let us divide equation 1 by (x+2) as follows:

(x2+4)(x+2)(x2)(x+2)=(x2+4)(x2)=x32x2+4x8

Hence, when the polynomial x416 is divided by (x+2) then the result is x32x2+4x8.

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