Question

Which of the following expressions are polynomials in one variable and which are not ? Give reasons for your answer.
(1) 3x²-2x+5 (2) x²+√2 (3) p²-3p+q(4) y+2/y(5) 5√x+x√5(6) x¹°°+y¹°°

Answer 1

Answer:

3x²-2x+5

x²+√2

y+2/y

5√x+x√5

Step-by-step explanation:

below are the polynomials in one variable as they have only one variable

3x²-2x+5

x²+√2

y+2/y

5√x+x√5

Below polynomials have two variables :

p²-3p+q   ( p & q)

x¹°°+y¹°°    (x & y)

Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

CONCEPT TO BE IMPLEMENTED

POLYNOMIAL

Polynomial is a mathematical expression consisting of constants, variables and exponents ( non negative integer) , that can be combined using addition, subtraction, multiplication

DEGREE OF A POLYNOMIAL

Degree of a polynomial is defined as the highest power of its variable that appears with nonzero coefficient

TO CHOOSE THE CORRECT OPTION

Check for polynomial in one variable

(1) 3x²-2x+5

(2) x²+√2

(3) p²-3p+q

$\displaystyle \: \sf{(4) \:y + \frac{2}{y} \: }$

$\displaystyle \: \sf{(5) \:5 \sqrt{x} + x \sqrt{5} \: }$

$\displaystyle \: \sf{(6) \: \: \: {x}^{100} + {y}^{100} \: }$

CALCULATION

CHECKING FOR OPTION (1)

$\displaystyle \: \sf{(1) \:3 {x}^{2} - 2x + 5 \: }$

Here the only variable is x and all the exponents are whole numbers

Hence it is a POLYNOMIAL

CHECKING FOR OPTION (2)

$\displaystyle \: \sf{(2) \: {x}^{2} + \sqrt{2} \: }$

Here is only one variable x and all the exponents are whole numbers

Hence it is a POLYNOMIAL

CHECKING FOR OPTION (3)

$\displaystyle \: \sf{(3) \: {p}^{2} - 3p + q \: }$

Here p and q are the two variables. All The exponents are whole numbers

Hence it is a POLYNOMIAL in two variables

CHECKING FOR OPTION (4)

$\displaystyle \: \sf{(4) \:y + \frac{2}{y} \: }$

$= \displaystyle \: \sf{\:y + 2 {y}^{ - 1} \: }$

Here is only one variable y and there is a exponent of y say - 1 which is not a whole number

Hence it is NOT A POLYNOMIAL

CHECKING FOR OPTION (5)

$\displaystyle \: \sf{(5) \: \: x \sqrt{5} + 5 \sqrt{x} \: }$

$\displaystyle \: \sf{ = \: \: x \sqrt{5} + 5 {x}^{ \frac{1}{2} } }$

Here is only one variable x but there is one exponent of x say 1/2 which is not a whole number

Hence it is NOT A POLYNOMIAL

$\displaystyle \: \sf{(6) \: \: {x}^{100} + {y}^{100} \: }$

Here is two variables x and y. Also the exponents are whole numbers

Hence it is a POLYNOMIAL of two variables

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LEARN MORE FROM BRAINLY

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x³-ax²+6x-a is divided by x - a

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