Question

point out which of the following expressions are polynomials? Justify your answer (i) 6x^2-3x+1 (ii) x^3-x^3+2x-2 (iii) 3x√x-5 (iv) 1/x^2+1/x-7 (v) √5x^3+1/3x+4 (iv) 3/x^3+6​

Answer 1

Answer:

Hey mate here is the answer

Step-by-step explanation:

plz check out the answer down

Correct answers with a reason:

• (I) - YESbecause the power of the variable is a whole number{the power of x is 2&1 which are while numbers}
• (ii) - YESbecause the power of the variable is a whole number{power of x is 1 as x^3 is eliminated by -x^3}
• (iii)-NO because its power is not a whole number {as here the power of x is 3/2 i.e x√x}
• (iv)-NO because after simplified it have no whole numbers as power
• (v)-YES because its power is a whole number {i.e x has power of 3 & 1 }
• (vi)-NO because when simplified the value changes to negative.

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Answer 2

Answer:

1) 6x²-3x+1 :- yes

2) x³-x³+2x-2 :- yes

3) 3x√x -5 :- no

4)1/x²+ 1/x -7 :- no

5) √5x³ + 1/3 x + 4 :- yes

6) 3/x³ + 6 :- no

Step-by-step explanation:

What is a Polynomial?

The expression of the form

$a_0 {x}^{0}+ a_1{x}^{1} + a_2 {x}^{2} + ... + a_n {x}^{n}$

is a polynomial in variable x of degree n where n is the largest power of x and n belong to Set of Whole numbers and where coefficients

$a_i \: i \: from \: 0 \: to \: n$

belong to set of Real numbers.

1)

$6 {x}^{2} - 3x + 1$

Yes, this expression is a Polynomial as all the coefficients are real and power of x are whole numbers.

2)

${x}^{3} - {x}^{3} + 2x - 2 = 2x - 2$

Yes, it a Polynomial. All the conditions are satisfied.

3)

$3x \sqrt{x} - 5 = 3 {x}^{ \frac{3}{2} } - 5$

No, it is not a Polynomial as one of the power of x is 3/2 and it is not a whole number.

4)

$\frac{1}{ {x}^{2} } + \frac{1}{x} - 7 = {x}^{ - 2} + {x}^{ - 1} - 7$

No, it is not a Polynomial. -2,-1 doesn't belong to the set of whole numbers.

5)

$\sqrt{5} {x}^{3} + \frac{1}{3} x + 4$

Yes, it is a Polynomial. All the conditions are satisfied. Coefficients are real and powers are whole numbers.

6)

$\frac{3}{ {x}^{3} } + 6 = 3 {x}^{ - 3} + 6$

No, it is not a Polynomial. Here power of x is -3 and -3 is not a whole number.

So (1),(2),(5) are polynomials and rest are not.