Which of following expressions are polynomials in one variable and which are not ? St

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2. Polynomials

easy

Which of the following expressions are polynomials in one variable and which are not $?$ State reason for your answer. If the given expression is a polynomial, state whether it is a polynomial in one variable or not

$x^{3}+y^{3}+z^{3}-3 x y z$

Option A

Option B

Option C

Option D

Solution

Given expression $x^{3}+y^{3}+z^{3}-3 x y z \quad$ is a polynomial because the total exponent of the variable in each of its terms is $3$ which is a whole number, but the given expression is expressed with three variables $x, y$ and $z .$ Therefore, the expression is not be a polynomial in one variable.

Standard 9

Mathematics

Verify whether $3$ and $5$ are zeros of the polynomial $x^{2}-x-6$ or not.

medium

For polynomial $p(x)=x^{3}-3 x^{2}+8 x+12$, $p(-1)=\ldots \ldots \ldots$

medium

Divide $p(x)=x^{3}+7 x^{2}+14 x+1$ by $x+3$ and find the quotient and the remainder.

medium

State whether each of the following statements is true or false

$x^{2}-8 x+12=(x-6)(x-2)$

easy

Factorise the following quadratic polynomials by splitting the middle term

$6 x^{2}+19 x+10$

medium

Which of the following expressions are polynomials in one variable and which are not $?$ State reason for your answer. If the given expression is a polynomial, state whether it is a polynomial in one variable or not $x^{3}+y^{3}+z^{3}-3 x y z$

Solution

Similar Questions

Verify whether $3$ and $5$ are zeros of the polynomial $x^{2}-x-6$ or not.

For polynomial $p(x)=x^{3}-3 x^{2}+8 x+12$, $p(-1)=\ldots \ldots \ldots$

Divide $p(x)=x^{3}+7 x^{2}+14 x+1$ by $x+3$ and find the quotient and the remainder.

State whether each of the following statements is true or false $x^{2}-8 x+12=(x-6)(x-2)$

Factorise the following quadratic polynomials by splitting the middle term $6 x^{2}+19 x+10$

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Which of the following expressions are polynomials in one variable and which are not $?$ State reason for your answer. If the given expression is a polynomial, state whether it is a polynomial in one variable or not

$x^{3}+y^{3}+z^{3}-3 x y z$

State whether each of the following statements is true or false

$x^{2}-8 x+12=(x-6)(x-2)$

Factorise the following quadratic polynomials by splitting the middle term

$6 x^{2}+19 x+10$