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If \( \Large a+b+c=0 \), thena \( \Large a^{3}+b^{3}+c^{3} \) is equal to

A) \( \Large a^{2} \left(b+c\right)+b^{2} \left(c+a\right)+c^{2} \left(a+b\right) \)
B) \( \Large 3 \left(b+c\right) \left(c+a\right) \left(a+b\right) \)
C) \( \Large 3 abc \)
D) \( \Large 6 a^{2}b^{2}c^{2} \)

Correct Answer:



C) \( \Large 3 abc \)

Description for Correct answer:

Given: \( \Large a+b+c=0 \)

=> \( \Large a+b = -c \)

Taking cube on both sides, we have

\( \Large \left(a+b\right)^{3} = \left(-c\right)^{3} \)

=> \( \Large a^{3}+b^{3}+3ab \left(a+b\right)=-c^{3} \)

=> \( \Large a^{3}+b^{3}+3ab \left(-c\right)=-c^{3} \)

=> \( \Large a^{3}+b^{3}+c^{3}=3abc \)

Part of solved Polynomials questions and answers : >> Elementary Mathematics >> Polynomials

Comments

Similar Questions

1). If \( \Large a^{m^{n}}= \left(a^{m}\right)^{n} \), then the value of m is

A). n

B). \( \Large \frac{n}{n^{n-1}} \)

C). \( \Large \frac{1}{n^{n-1}} \)

D). \( \Large n^{\frac{n-1}{n}} \)

2). Value of \( \Large \left(X^{b-c}\right)^{b+c},\ \left(X^{c-a}\right)^{c+a},\ \left(X^{a-b}\right)^{a+b} \) is

A). 0

B). X

C). 1

D). X+1

3). If \( \Large 2^{x}=4^{y}=8^{z} and \frac{1}{2x}+\frac{1}{4y}+\frac{1}{6z}=\frac{24}{7} \), then value of z is

A). \( \Large \frac{7}{16} \)

B). \( \Large \frac{7}{32} \)

C). \( \Large \frac{7}{48} \)

D). \( \Large \frac{7}{46} \)

4). Which one of the following is a polynomial?

A). \( \Large x^{3}+\sqrt{3x^{2}}+4\sqrt{x} \)

B). \( \Large x^{6}+2\sqrt{x^{2}}+x^{-1} \)

C). \( \Large x^{5}+x^{4}+x^{-1}+x^{-5} \)

D). \( \Large x^{3}+\sqrt{5x^{2}}+x+\sqrt{3} \)

5). If \( \Large X^{y}=Y^{z} \), then \( \Large \left(\frac{Y}{X}\right)^{\frac{x}{y}} \) equals

A). \( \Large X^{\frac{x}{y}} \)

B). \( \Large X^{ \left(\frac{x}{y}\right)-1 } \)

C). \( \Large X^{\frac{y}{x}} \)

D). \( \Large X^{1-\frac{x}{y}} \)

6). If \( \Large x+\frac{1}{x}=3 \), then value of \( \Large x^{3}+\frac{1}{x^{3}} \) is

A). 18

B). 24

C). 27

D). 36

7). If \( \Large x^{5}-9x^{2}+12x-14 \) is divided by \( \Large x-3 \), then the remainder is

A). 1

B). 2

C). 56

D). 184

8). If polynomial \( \Large f \left(x\right) \) is such that \( \Large f \left(-2\right)=0 \), then which of the following is always a factor of \( \Large f \left(x\right) \)?

A). 2x

B). 2-x

C). x+2

D). x-2

9). If \( \Large x^{2}+ax+b \) leaves the same remainder 5 when divided by x-1 or x+1, then values of 'a' and 'b' are respectively.

A). 0 and 4

B). 3 and 0

C). 0 and 3

D). 4 and 0

10). Product of zeroes of the polynomial \( \Large x^{3}-6x^{2}+11x-6 \) is

A). 11

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