Divide 5x^3-x^2+6 by x-4 . Verify the solution also.

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Solution

5x^2 +19x+76
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x-4 | 5x^3 -x^2 +0x +6
5x^3 -20x^2
--------------------
19x^2 +0x
19x^2 -76x
--------------
76x+6
76x-304
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310

Quotient = 5x^2+19x+76 and remainder = 310
Verify remainder using Remainder theorem
Substitute x = 4 into polynomial. We get:
5(4)^3-(4)^2 + 6 = 5(64)-16+6 = 320-16+6 = 310
So it is verified

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