Question

find a and b so that x^2-1 is a factor of x^4 + ax^3+ 2x^2- 3x+ b

Answer 1

to solve this we have to solve value of x from the given factor, then put the value in the polynomial
${x}^{2} - 1 = 0 \\ {x}^{2} = 1 \\ x = \sqrt{1}$
so value of x= -1 and +1
${x}^{4} + a {x}^{3} + 2 {x}^{2} - 3x + b \\ put \: x = - 1 \\ 1 - a + 2 + 3 + b = 0$
$- a + b = - 6 \: \: \: \: ....eq \: 1 \\ put \: x = 1 \\ 1 + a + 2 - 3 + b = 0$
$a + b = 0 \: \: \: \: ....eq \: 2 \\ from \: eq \: 1 \: and \: eq \: 2 \: calculate \: the \: \\ value \: of \: a \: and \: b$
on adding both equation,we get
$2b = - 6 \\ b = - 3$
put the value of B in any equation for value of a
$a - 3 = 0 \\ a = 3$
so these are the values of a and b.
hope it may help you.