Question

- - 14. The polynomial p(x) = x+ - 2x + 3x² - ax + b when divided by (x - 1) and (x +1) leaves the remainders 5 and 19 respectively. Find the values of a and b. Hence, find the remainder when p(x) is divided by (x-2).​

Answer 1

Answer:

When p(x) is divided by (x-2),the remainder obtained is 10

Step-by-step explanation:

Given that, the polynomial leaves the remainders 5 and 19 when divided by (x-1) and (x-(-1))

Now, according to the remainder theorem if a polynomial p(x) is divided by (x-a),the remainder obtained is p(a)

So, we have p(1) = 5 and p(-1) = 19

from the equation p(1) = 5 we have (1)⁴ -2(1)³ +3(1)² -a(1)+b = 5

or, b-a = 3

and from the equation p(-1) = 19 we have (-1)⁴ - 2 (-1) ³ + 3(-1)² -a(-1) +b = 19

or a+b = 13

On solving a+b = 13 and b-a = 3

we get, a= 5 and b=8

Hence, when divided by (x-2)

→ p(2) = (2)⁴ - 2(2)³ + 3(2)² -5*2 +8 = 10