Determine the degree of each of the following polynomials:(i) 2x – 1

1.	Determine the degree of each of the following polynomials:(i) 2x – 1(ii) –10(iii) x3 – 9x + 3x5(iv) y3 (1 – y4)
Answer» Degree of a polynomial in one variable = highest power of the variable in algebraic expression (i) 2x – 1 Power of x = 1 Highest power of the variable x in the given expression = 1 Hence, degree of the polynomial 2x – 1 = 1 (ii) –10 There is no variable in the given term. Let us assume that the variable in the given expression is x. – 10 = –10x⁰ Power of x = 0 Highest power of the variable x in the given expression = 0 Hence, degree of the polynomial – 10 = 0 (iii) x³ – 9x + 3x⁵ Powers of x = 3, 1 and 5 respectively. Highest power of the variable x in the given expression = 5 Hence, degree of the polynomial x³ – 9x + 3x⁵= 5 (iv) y³ (1 – y⁴) The equation can be written as, y³ (1 – y⁴) = y³ – y⁷ Powers of y = 3 and 7 respectively. Highest power of the variable y in the given expression = 7 Hence, degree of the polynomial y³ (1 – y⁴) = 7

Determine the degree of each of the following polynomials:(i) 2x – 1(ii) –10(iii) x3 – 9x + 3x5(iv) y3 (1 – y4)

Answer»

Degree of a polynomial in one variable = highest power of the variable in algebraic expression

(i) 2x – 1

Power of x = 1

Highest power of the variable x in the given expression = 1

Hence, degree of the polynomial 2x – 1 = 1

(ii) –10

There is no variable in the given term.

Let us assume that the variable in the given expression is x.

– 10 = –10x⁰

Power of x = 0

Highest power of the variable x in the given expression = 0

Hence, degree of the polynomial – 10 = 0

(iii) x³ – 9x + 3x⁵

Powers of x = 3, 1 and 5 respectively.

Highest power of the variable x in the given expression = 5

Hence, degree of the polynomial x³ – 9x + 3x⁵= 5

(iv) y³ (1 – y⁴)

The equation can be written as,

y³ (1 – y⁴) = y³ – y⁷

Powers of y = 3 and 7 respectively.

Highest power of the variable y in the given expression = 7

Hence, degree of the polynomial y³ (1 – y⁴) = 7