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find the remainder on dividing x 3 +1 by x+1

Posted by Krishnanandha Ar 4 years, 3 months ago

CBSE > Class 09 > Mathematics

1 answers

Gaurav Seth 4 years, 3 months ago

Long division

x^2 - x + 1
____________
x+1 [ x^3 + 1
[ x^3 + x^2
----------------
-x^2 + 1
-x^2 - x
------------
x + 1
x + 1
----------

0

so, the answer is:

x² - x + 1

Using factor theorm:

a³ + b³ = (a + b)(a² – ab + b²)

So, x³ + 1 = x³ + 1³ = (x+1)(x² - 2x + 1)

and (x³ + 1) / (x+ 1) = (x+1)(x² - 2x + 1) / (x + 1)

The (x + 1) brackets cancel out and we are left with

x² - 2x + 1

0Thank You

ANSWER

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CBSE > Class 09 > Mathematics