Question

Choose the polynomial that is written in standard form.

a) 2x2y2 + 3x4y + 10x6

b) 4x4y2 + 6x3y5 + 10x

c) −3x8y2 + 9x2y + 10x2

d) −7x6y2 + x3y8 + 10x2

Answer 1

C)
`-3x^8y^2+9x^2y+10x^2`

Explanation:

Since, a polynomial having the descending order of degrees of the monomial is called the standard polynomial,

Also, the degree of a term in the polynomial is the total sum of the power of all variable in that term,

In option a),

`2x^2y^2 + 3x^4y + 10x^6`

Order of degree is,

4, 5, 6

Which is not in the descending order,

⇒ It is not a standard polynomial.

In option b),

`4x4y^2 + 6x^3y^5 + 10x`

Order of degree is,

5, 8, 1

Which is not in the descending order,

⇒ It is not a standard polynomial.

In option c),

`-3x^8y^2 + 9x^2y + 10x^2`

Order of degree is,

11, 3, 2

Which is in the descending order,

⇒ It is a standard polynomial.

In option d),

`-7x^6y^2 + x^3y^8 + 10x^2`

Order of degree is,

8, 11, 2

Which is not in the descending order,

⇒ It is not a standard polynomial.

Answer 2

The degrees of the terms are ...
a) 4, 5, 6
b) 6, 8, 1
c) 10, 3, 2
d) 8, 11, 2

The polynomial that has terms in decreasing order of degree is
c) -3x⁸y² +9x²y +10x²