Question

The polynomials 2x3 + x2 – a x +2 and 2x3 – 3x2 – 3x +a when divided by (x-2) leave the
same remainder. Find the value of a

Answer 1

Answer:

See the attachment

Step-by-step explanation:

Answer 2

Answer:

a = 8

Step-by-step explanation:

let p(x) = $2x^{3} + x^{2} - ax + 2$

let f(x) = $2x^{3} - 3x^{2} - 3x + a$

g(x) = x - 2

x - 2 = 0

x = 2

Substitute x in p(x),

$2(2)^{3} + (2)^{2} - a(2) + 2 = 0$

$16 + 4 - 2a + 2 = 0$

$22 - 2a = 0$          --(1)

Substitute x in f(x)

$2(2)^{3} - 3(2)^{2} - 3(2) + a = 0$

$16 - 12 - 6 + a = 0$

$-2 + a = 0$          --(2)

Equate (1) and (2)

22 - 2a = -2 + a

24 = a + 2a

a = 24/3

a = 8