Let, r, s and t be real numbers such that r + t \neq s, what is the quotient on dividing r ^3 - s^ 3 + t ^3 + 3rst by (r - s + t)?

Correct Answer is : r2−s2+t2+rs+st−rt

Algebra and Applications Test 1

Question : 23 of 40

Marks: +1, -0

Let, r, s and t be real numbers such that

r + t ≠ s

, what is the quotient on dividing

r ^3 - s^ 3 + t ^3 + 3rst

(r - s + t)

Solution:

We know that

r^3 - s^3 + t^3 + 3 rst = (r - s + t) (r^2 - s^2 + t^2 +rs + st - rt)

This shows that when

r^3 - s^3 + t^3 + 3 rst

is divided by

(r - s + t)

, the quotient is

r^2 - s^2 + t^2+ rs + st - rt)

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