Question

if both ( x+1)and (x-1) are factors of ax^3 +x^2 -2x+b ,find a and b​

Answer 1

Answer:

(x+1)and (x-1) are factors therfore

p(1) and p(-1) is equal to zero

$a {1}^{3} + {1}^{2} - 2(1) + b = 0 \\ a + 1 - 2 + b = 0 \\ a + b = 1 \\ a { (- 1)}^{3} + { (- 1)}^{2} - 2( - 1) + b = 0 \\ - a + 1 + 2 + b = 0 \\ - a + b = - 3 \\ adding \: both \: the \: eqations \\ a + b - a + b = 1 - 3 \\ 2b = - 2 \\ b = - 1 \\ \\ a + b = 1 \\ a - 1 = 1 \\ a = 2$