Algebra and Applications Test 1

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Question : 31 of 40

Marks: +1, -0

When

x + y + z + 3x ^{1/3} y ^{2/3} + 3x^{ 2/3} y ^{1/3}

is divided by

x^{1/3} + y^{1/3} + z ^{1/3}

, what is the remainder?

3x
3y
0
$z ^{2/3 }$
None of these

Solution:

Let

f(a) = x + y + z + 3x^{1/3} y^{2/3} + 3x^{2/3} y^{1/3}

= x^{1/3} + y^{1/3})^3 + (z^{1/3})^3

Now remainder

= f(x^{1/3} + y^{1/3})

= (-z^{1/3})^3 + (z^{1/3})^3

= -z + z = 0

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