Question

the polynomials
$(2x {}^{3} + x {}^{2} - ax + 2$
and
$(2x {}^{3} - 3x {}^{2} - 3x + a)$
when divided by (x-2) leave the same remainder. Find the value of 'a'.​

Answer 1

Answer:

Let the given polynomial be f(x) & g(x). When f(x) & g(x) are divided by (x-2) they have the same remainder

x - 2 = 0 ; x = 2

So, f(2)= g(2)

2x³ + x²- ax + 2 = 2x³ - 3x² - 3x + a

2(2)³ + (2)² - a(2) + 2 = 2(2)³ - 3(2)² - 3(2) + a

16 + 4 - 2a + 2 = 16 - 12 - 6 + a

22 - 2a = -2 + a

-2a - a = -2 - 22

- 3a = -24

a = 24/3

a = 8