Question

1. Point out which of the following expressions are polynomials with reasons.
(1) 5x2 - 2x + 1
(2)x³-8
(3)⁷/x²+2x+1
(4)3x+5✓x-7​

Answer 1

Answer:

1. Yes bcoz the variable x does not have any negative power nor it does not have any fractional exponent.

2. Yes...Reason same as above

3. No bcoz x^2 is in the denominator so when taken in the numerator it will be x^(-2) which is negative power and is not acceptable.

4. No bcoz here x has fractional power here i.e. x^(1/2)

which is not acceptable.

Answer 2

Answer:

Step-by-step explanation:

A polynomial can have constants, variables and exponents, but never division by a variable.

A polynomial can't have a negative exponent.

Polynomials can have no variable at all, or one variable or two or more variables.exponents can only be 0,1,2 or multiples not in fractions.

(1) $5x^{2} -2x +1$ - This is a polynomail as it satisfies all the conditions above. Also x doesn't have a negative exponent.

(2) $x^{3} -8$ This is also a polynomial as 3 is not a negative exponent

(3) ⁷/x²+2x+1  This is not a polynomial as x when carried up has a negative value which deoesn't satisfy our statement of positive exponent.

(4) 3x+5✓x-7  This is also not a polynomial as x when removed the root, its power becomes 1/2 which doesn't satisfy our condition of whole no. exponents.

Hope it helps mate....

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