COEFFICIENTS AND DEGREE OF A POLYNOMIAL

Question 1 :

Write the coefficient of x² and x in each of the following polynomials.

(i)  4 + (2/5)x² - 3x

Solution :

Coefficient of x²  =  2/5

Coefficient of x  =  -3

(ii) 6 - 2x² + 3x³ - √7 x

Solution :

Coefficient of x²  =  -2

Coefficient of x  =  -√7

(iii)  π x² - x + 2

Solution :

Coefficient of x²  =  π

Coefficient of x  =  -1

(iv)  √3 x² + √2x + 0.5

Solution :

Coefficient of x²  =  √3

Coefficient of x  =  √2

(v)  x² - (7/2)x + 8

Solution :

Coefficient of x²  =  1

Coefficient of x  =  -7/2

Question 2 :

Find the degree of the following polynomials.

(i)  1 - √2y² + y⁷

Solution :

The highest power of y is 7. Hence the degree of the polynomial is 7.

(ii)  (x³ - x⁴ + 6x⁶)/x²

Solution :

  =  (x³ - x⁴ + 6x⁶)/x²

  =  x - x² + 6x⁴

The highest power of x is 4. Hence the degree of the polynomial is 4.

(iii)  x³ (x² + x)

Solution :

  =  x³ (x² + x)

  =  x⁵ + x⁴ 

The highest power of x is 5. Hence the degree of the polynomial is 5.

(iv)  3x⁴ + 9x² + 27x⁶ 

Solution :

  =  3x⁴ + 9x² + 27x⁶ 

The highest power of x is 6. Hence the degree of the polynomial is 6.

(v)  2√5p⁴ - (8p³/√3) + (2p²/7)

Solution :

  =  2√5p⁴ - (8p³/√3) + (2p²/7)

The highest power of p is 4. Hence the degree of the polynomial is 4.

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