Question

(3x²)³ (3 y)
(3x)³ (3x)²​

Answer 1

Answer:

(i) x⁵ – x⁴ + 3,

The highest power of the variable is 5. So, the degree of the polynomial is 5.

(ii) 2 – y² – y³ + 2y⁸,

The highest power of the variable is 8. So, the degree of the polynomial is 8.

(iii) 2 .

There is no any variable with 2. Therefore, the degree of the polynomial is 0.

Example-2 :- Find the value of each of the following polynomials at the indicated value of variables:

(i) p(x) = 5x² – 3x + 7 at x = 1.

(ii) q(y) = 3y³ – 4y + √11 at y = 2.

(iii) p(t) = 4t⁴ + 5t³ – t² + 6 at t = a.

Solution :-

(i) p(x) = 5x² – 3x + 7 at x = 1.

p(1) = 5 x (1)² - 3 x 1 + 7

= 5 - 3 + 7

= 12 - 3

= 9

(ii) q(y) = 3y³ – 4y + √11 at y = 2.

q(2) = 3 x (2)³ – 4 x 2 + √11

= 3 x 8 - 8 + √11

= 24 - 8 + √11

= 16 - √11

(iii) p(t) = 4t⁴ + 5t³ – t² + 6 at t = a.

p(a) = 4 x (a)⁴ + 5 x (a)³ – (a)² + 6

= 4a⁴ + 5a³ – a² + 6

Example-3 :- : Check whether –2 and 2 are zeroes of the polynomial x + 2.

Solution :-

Let p(x) = x + 2 at x = -2

p(-2) = -2 + 2 = 0

Now, p(x) = x + 2 at x = 2

p(2) = 2 + 2 = 4

So, -2 is zeroe of polynomial x + 2, but 2 is not.

Example-4 :- Find a zero of the polynomial p(x) = 2x + 1.

Solution :-

p(x) = 2x + 1. Finding for zero p(x) = 0

0 = 2x + 1

-1 = 2x

-1/2 = x

x = -1/2

The zero of polynomial p(x) = 2x + 1 is -1/2.

Example-5 :- Verify whether 2 and 0 are zeroes of the polynomial x² – 2x.

Solution :-

Let p(x) = x² – 2x at x = 2

p(2) = (2)² + 2

= 4 + 2

Answer 2

Answer:

4+2is the last answer......