Q2 of 64 Page 30

Obtain the degree of the following polynomials:

(1) p(x) = 3x —x4 + x2 + 2x3 + 7


(2) p(x) = x3 — 3x —x2 + 6


(3) p(x) = 3x — 9


(4) p(x) = 2x2 — x + 1

(1) Here p(x) = 3x —x4 + x2 + 2x3 + 7


Highest power of x in the above expression is 4. Hence, the degree of the polynomial is 4.


(2) Here p(x) = x3 — 3x —x2 + 6


Highest power of x in the above expression is 3. Hence, the degree of the polynomial is 3.


(3) Here p(x) = 3x — 9


Highest power of x in the above expression is 1. Hence, the degree of the polynomial is 1.


(4) Here p(x) = 2x2 — x + 1


(5) Highest power of x in the above expression is 2. Hence, the degree of the polynomial is 2.


More from this chapter

All 64 →
1

Identify the type of the following polynomials: (on base of power)

(1) p(x) = x2 — 5x + 6


(2) p(x) = x2 — x3 + x + 1


(3) p(x) = 5x2 + 8x + 3


(4) p(x) = x3

 3

Find the coefficients of the underlined terms:

(1) p(x) = 10x3+ 7 x2 — 3x + 5


(2) p(x) = 7 — 5x5+ 3x4 + x2 — x


(3) p(x) = 25 — 125x


(4) p(x) = x3 — x2 + x + 7

 4

Obtain the value of the following polynomials at the given values of x:

(1) p(x) = 2x3 + 3x2 + 7x + 9 ; at x = 0, 1


(2) p(x) = 3x2 + 10x + 7 ; at x = —3, 1


(3) p(x) = x2 — 2x + 5 ; at x = —1, 5


(4) p(x) = 2x4 — 3x3 + 7x + 5 ; at x = —2, 2

 5

Examine the validity of the following statements:

(x + 1) is a factor of p(x) = 3x3 + 2x2 + 7 x + 8