Which is not a polynomial function?a. y=3x^2+2x+1/2 b. y=10X+8 c. y= t^2+2t-4/ 2t-1 it would be c right because a is a 2nd degree function, b is a linear function and c doesn't fit a description

2 Answers

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

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A polynomial is a sum of finite number terms with real coefficients and non negative or positive integral powers of the variable.

The polynomial can not have fractional  power of the variable. A polynomial has no terms with negative exponents of the variable.

A polynomial can have one term. It can have two or more terms also.

A polynomial can be with single variable or many variables. If the highest of the term and the degree of the polynomial are the same.

c is not a polynomial in the given set, as it conains a term -4/t whose degree is -1 as -4/t =  -4t^(-1). The exponent of the variable t of this term is -1 , a negative exponent. A polynomial does not have a term with a negative exponent variable.

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william1941 | College Teacher | (Level 3) Valedictorian

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A polynomial function is of the form that can be represented as:

f(x) = A1*x^n + A2*x^(n-1)....An*x^0

Now looking at the three functions given:

a. y = 3x^2 + 2x + 1/2 = 3x^2 + 2x + 0.5

This is a polynomial as it fits in the format given exactly.

b. y = 10X + 8

This also is a polynomial as it also fits into the format given.

c. y= t^2 + 2t - 4/ 2t-1

Here y = t^2 + 2t - 4/ (2t-1)

This cannot be expressed as the sum of a series of terms with a decreasing power of t due to the term (2t-1) which lies in the denominator.

Hence the option c is not a polynomial.