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+ \{ 2 }{ y }
(v) x10+ y3+t50
Give a proper answer.
Answers
(i) We have 4x2 – 3x + 7 = 4x2 – 3x + 7x0
It is a polynomial in one variable i.e., x
because each exponent of x is a whole number.
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(ii) We have y2 + √2 = y2 + √2y0
It is a polynomial in one variable i.e., y
because each exponent of y is a whole number.
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(iii) We have 3 √t + t√2 = 3 √t ½ + √2.t
It is not a polynomial, because one of the exponents of t is \frac { 1 }{ 2 },
which is not a whole number.
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(iv) We have y + y+ + 2.y-1
It is not a polynomial, because one of the exponents of y is -1,
which is not a whole number.
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(v) We have x10+ y3 + t50
Here, exponent of every variable is a whole number, but x10 + y3 + t50 is a polynomial in x, y and t, i.e., in three variables.
So, it is not a polynomial in one variable.
(i) We have 4x2 – 3x + 7 = 4x2 – 3x + 7x0
It is a polynomial in one variable i.e., x
because each exponent of x is a whole number.
▬▬▬▬▬▬▬▬▬▬▬▬
(ii) We have y2 + √2 = y2 + √2y0
It is a polynomial in one variable i.e., y
because each exponent of y is a whole number.
▬▬▬▬▬▬▬▬▬▬▬▬
(iii) We have 3 √t + t√2 = 3 √t ½ + √2.t
It is not a polynomial, because one of the exponents of t is \frac { 1 }{ 2 },
which is not a whole number.
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(iv) We have y + y+ + 2.y-1
It is not a polynomial, because one of the exponents of y is -1,
which is not a whole number.
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(v) We have x10+ y3 + t50
Here, exponent of every variable is a whole number, but x10 + y3 + t50 is a polynomial in x, y and t, i.e., in three variables.
So, it is not a polynomial in one variable.