Question

02.A.Given that (x+2) and (x-1) are the factors of x^(3)+ax^(2)+x-b calculate the values of a and b and hence find the remaining factor of the given polynomial.​

Answer 1

Answer:

Find the remainder (without division) on dividing f(x) by (x – 2) where

(i) f(x) = 5x2 – 7x + 4

Solutions:-

Let us assume x – 2 = 0

Then, x = 2

Given, f(x) = 5x2 – 7x + 4

Now, substitute the value of x in f(x),

f(2)= (5 × 22) – (7 × 2) + 4

= (5 × 4) – 14 + 4

= 20 – 14 + 4

= 24 – 14

= 10

Therefore, the remainder is 10.

(ii) f(x) = 2x3 – 7x2 + 3

Solution:-

Let us assume x – 2 = 0

Then, x = 2

Given, f(x) = 2x3 – 7x2 + 3

Now, substitute the value of x in f(x),

f(2)= (2 × 23) – (7 × 22) + 3

= (2 × 8) – (7 × 4) + 3

= 16 – 28 + 3

= 19 – 28

= -9

Therefore, the remainder is -9.