. Degree of Polynomial 5x – 7x3 + 9x5 – 2x6 – 3x2 + 2 is

1.	. Degree of Polynomial 5x – 7x3 + 9x5 – 2x6 – 3x2 + 2 is
Answer» GIVEN, The polynomial $5x\:-7x^3\:+9x^5\:-2x^6\:-3x^2\:+2$ . To Find, The degree of the given polynomial. Solution, → The degree of the polynomial refers to the highest constant exponent in the polynomial. → Here, we can ARRANGE all the EXPONENTS in the ascending order. We get: 0, 1, 2, 3, 5 and 6 → In the exponents ARRANGED in ascending order, we can see that the highest exponent is 6 with the base 2x. → Therefore the degree of the given polynomial is sextic with the degree of 6. → So, $5x\:-7x^3\:+9x^5\:-2x^6\:-3x^2\:+2$ is a sextic polynomial (a polynomial of degree 6). Knowledge Bytes: → The degree of the polynomial refers to the highest exponent in the given polynomial. On the basis of the degree of the polynomial, the polynomials are classified as follows: ✳ Constant polynomial - A polynomial of degree 0 is known as constant polynomial. ✳ Linear polynomial - A polynomial of degree 1 is known as linear polynomial. ✳ QUADRATIC polynomial - A polynomial of degree 2 is known as a quadratic polynomial. ✳ Cubic polynomial - A polynomial of degree 3 is known as cubic polynomial. ✳ Quartic polynomial - A polynomial of degree 4 is known as quartic polynomial. ✳ Quintic polynomial - A polynomial of degree 5 is known as a quintic polynomial and so on...

Answer»

GIVEN,

The polynomial $5x\:-7x^3\:+9x^5\:-2x^6\:-3x^2\:+2$ .

To Find,

The degree of the given polynomial.

Solution,

→ The degree of the polynomial refers to the highest constant exponent in the polynomial.

→ Here, we can ARRANGE all the EXPONENTS in the ascending order. We get:

0, 1, 2, 3, 5 and 6

→ In the exponents ARRANGED in ascending order, we can see that the highest exponent is 6 with the base 2x.

→ Therefore the degree of the given polynomial is sextic with the degree of 6.

→ So, $5x\:-7x^3\:+9x^5\:-2x^6\:-3x^2\:+2$ is a sextic polynomial (a polynomial of degree 6).

Knowledge Bytes:

→ The degree of the polynomial refers to the highest exponent in the given polynomial. On the basis of the degree of the polynomial, the polynomials are classified as follows:

✳ Constant polynomial - A polynomial of degree 0 is known as constant polynomial.

✳ Linear polynomial - A polynomial of degree 1 is known as linear polynomial.

✳ QUADRATIC polynomial - A polynomial of degree 2 is known as a quadratic polynomial.

✳ Cubic polynomial - A polynomial of degree 3 is known as cubic polynomial.

✳ Quartic polynomial - A polynomial of degree 4 is known as quartic polynomial.

✳ Quintic polynomial - A polynomial of degree 5 is known as a quintic polynomial and so on...