Question

(x ^ 2) ^ (1/2) + 2sqrt(5) a polynomial?​

Answer 1

Question:

Is (x²)½ + 2√5 a polynomial?

Answer:

Yes, it is a polynomial.

Explanation:

(x²)½ + 2√5

√5 can be written as 5½

= (x²)½ + 2(5)½

= ( x )² * ½ + 2(5)½

= x¹ + 2(5)½

= x + 2(5)½

We can see it is of the form form ax + b. The exponent of the variable x is a 1 which is a whole number, so it is a linear polynomial.

Note that: we might think 5 has an exponent that is not a whole number i.e. 1/2, So it must not be a polynomial. But the power of a "variable" must be a whole number, there's no condition over constants. In this case 2(5)½ is the coefficient of a variable having a zero Exponent.

Overview of polynomials:

Polynomial is an algebraic expression that contains one or more terms. The exponents of the variable should be whole numbers.

Whole numbers: 0, 1, 2, 3 . . . . ∞

General form of a polynomial in one variable:-

axⁿ, bxⁿ⁻¹, cxⁿ⁻², dxⁿ⁻³. . . .

Where a is the numeric coefficient and x is the variable.

General form of a linear polynomial:-

ax + b

General form of a quadratic polynomial:-

ax² + bx + c

General form of a cubic polynomial:-

ax³ + bx² + cx + d