Practice Questions

P(x) = ax³ + bx² + cx + d

P(1) = P(x) = a× 1³ + b× 1 ² + c× 1 + d

= a + b + c + d

P(-1) = a× -1³ + b× -1 ² + c× -1 + d

= -a + b -c + d

Since P(1) = P( -1)

a + b + c + d = -a + b + -c + d

2a + 2c = 0

a + c = 0

P(x) = 2x³ - 7x² + kx + 20

P(2) = 2(2)³ - 7(2)² + k(2) + 20

=  16 - 28 + 2k + 20

= 8 + 2k

P(3) =  2(3)³ - 7(3)² + k(3) + 20

= 54 - 63 + 3k + 20

= 11 + 3k

P(2) = P(3)

8 + 2k = 11 + 3k

k = -3

P(x) = 2x³ + 9x² + kx + 3, P(-2) = P(-3)

P(-2) = 2(-2)³ + 9(-2)² + k(-2) + 3

= -16 + 36 -2k + 3

= 23 - 2k

P(-3) = 2(-3)³ + 9(-3)² + k(-3) + 3

= -54 + 81 -3k + 3

= 30 - 3k

Since P(-2) =P(-3)

23 - 2k = 30 - 3k

k = 7

P(x)= ax² + bx + c 

P(0) = c =0 ...... (1)

P(1) = a + b + c =1 .........(2)

P(2) = a × 2²  + b × 2 + c = 6

4a + 2b + c =6

4a + 2b = 6

2a + b = 3 ..........(3)

from (2) and (3)

a = 2

b = -1

So ,

P(x) = 2x² + -1x = 0

The first degree polynomial with P(1)=1 and P(3)=2:

P(x) = ax + b

P(1)= 1

⇒ a + b = 1 .......(1)

P(3)= 2

⇒ 3a + b = 2 ......(2)

From (1) and (2)

2a = 1 ⇒ a = 1/2

from (1) b = 1/2

So P(x) = ax + b = 1/2x + 1/2

The value of the greatest exponent for a polynomial written in standard form is called 
the degree of polynomial

Here degree = 6

The value of the greatest exponent for a polynomial written in standard form is called 
the degree of polynomial

So here degree of the polynomial = 4

The value of the greatest exponent for a polynomial written in standard form is called 

- Degree of polynomial

A expression containing one or more terms with non - zero coefficient is called a Polynomials 

Eg : x³ + x² + 2x + 1

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