Exercise 8.1
1. Write the degree of each of the following polynomials:
(i) 2x³ + 5x2– 7
(ii) 5x2 – 35x + 2
(iii) 2x + x2 – 8
(iv) (1/2)y7 -12y6 + 48y5 − 10
(v) 3x3 + 1
(vi) 5
(vii) 20x3 + 12x2y2 – 10y2 + 20
Solution:
(i) 2x³+5x2-7
It is 2x³+5x2-7 instead of 2x2+5x2-7
The degree of the polynomial 2x³+5x2-7 is 3
(ii) 5x2-35x+2
The degree of the polynomial 5x2-35x+2 is 2
(iii) 2x+x2-8
The degree of the polynomial 2x+x2-8 is 2
(iv) 12y7−12y6+48y5−10
The degree of the polynomial 12y7−12y6+48y5−10 is 7
(v) 3x3+1
The degree of the polynomial 3x3+1 is 3
(vi) 5
5 is a constant polynomial and its degree is 0.
(vii) 20x3+12x2y2-10y2+20
The degree of the polynomial 20x3+12x2y2-10y2+20 is 4
2. Which of the following expressions are not polynomials:
Solution:
(i) x2 + 2x-2
x2 + 2x-2 is not a polynomials because -2 is the power of variable x is not a non negative integer.
3. Write each of the following polynomials in the standard from. Also, write their degree:
Solution:
(i) (x2+3+6x+5x4)
The standard form of the given polynomial can be expressed as:
(5x4+x2+6x+3) or (3+6x+x2+5x4)
The degree of the polynomial is 4
(ii) a2+4+5a6
The standard form of the given polynomial can be expressed as:
(5a6+a2+4) or (4+a2+5a6)
The degree of the polynomial is 6
(iii) (x3-1)(x3-4)
(x3-1)(x3-4) = x6-5x3+4
The standard form of the given polynomial can be expressed as:
(x6-5x3+4) or (4-5x3+x6)
The degree of the polynomial is 6
(iv) (y3-2)(y3+11)
(y3-2)(y3+11) = y6+9y3-22
The standard form of the given polynomial can be expressed as:
(y6+9y3-22) or (-22+9y3+y6)
The degree of the polynomial is 6