Question

answer with step pls pls pls........

Answer 1

HERE IS YOUR ANSWER.
$p(x) = {x}^{4} - 2 {x}^{3} + 3 {x}^{2} - ax + b$
Now by remainder theorem,
when p(x) is divided by x - 1,
$remainder \: = p(1) = {1}^{4} - 2 \times {1}^{3} + 3 \times {1}^{2} - a \times 1 + b \\ = 1 - 2 + 3 - a + b = 5 \\ = > b - a = 3 \: \: ............(1)$
and, when p(x) is divided by x + 1,
$remainder \: = p( - 1) = { (- 1)}^{4} - 2 \times {( - 1)}^{3} + 3 \times {( - 1)}^{2} - a \times ( - 1) + b \\ = > 1 + 2 + 3 + a + b = 19 \\ = > a + b = 14 \: \: \: ...............(2)$
solving equations (1) and (2), we get,

b = 17/2
a = 11/2
so now you can do polynomial division, i.e.,
divide p(x) by (x -2) to get the answer.


Hope it clears your doubts.