Question

Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.
(i) 4x2 – 3x + 7
(ii) y2 + √2
(iii) 3 √t + t√2
(iv) y+ 2y
(v) x10+ y3+t50







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Answer 1

Explanation:

i) 4x² - 3x + 7

The given polynomial has one variable 'x'.

Thus, 4x² - 3x + 7 is a polynomial in one variable.

ii) y² + √2

The given polynomial has one variable 'y'.

Thus, y² + √2 is a polynomial in one variable.

iii) 3√t + t√2

3t1/2 + t√2 is not a polynomial, since the power of the variable in the first term is 1/2 which is not a whole number.

iv) y + (2/y)

y + 2y-1 is not a polynomial since the power of the variable in the second term is -1 which is not a whole number.

v) x10 + y3 + t50

x10+ y3+ t50 is not a polynomial in one variable since there are 3 variables x, y, and t.

I hope it helps you

Answer 2

Answer:

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)

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

$= \displaystyle \: \sf{\:y + 2 {y}^{ - 1} \: }</p><p>$

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

Explanation:

Hope it helps (~‾▿‾)~