Question

Show that x+2 and x-3 are the factors of x3 +ax+b​

Answer 1

Answer:

if X+2 and x-3 are factors then equation satisfy factors

Step-by-step explanation:

x+2=0 and x-3,=0

$x = - 2$

$x = 3$

${3}^{3} + a \times 3 + b$

$27 + 3a + b = 0$

$3a + b = - 27$

for

$x = - 2$

${ - 2}^{3} - 2a + b = 0$

$- 2a + b = 8$

$a = - 7$

$b = - 6$

Answer 2

Answer:

hey there!!!!!!

Step-by-step explanation: x+2 , x-3 are to show the factors of x^3+ax+b

   so;  x = -2 , x= 3

putting x= -2 in x^3+ax+b

then b-2a = 8..................equation 1

putting x= 3

then, 3a+ b = -27.................equation 2

substracting eqn 1 from eqn 2:

we get 5a = 35

a = 7 , and by putting the value of a in one of them i.e eqn 1 and 2:

we get : b = 22

putting the value of a and b in eqn x^3+ax+b

we get, x^3+7x+22

when we divide x^3+7x+22 with x+2 and x-3 alternately we get remainder as 'zero' .

therefore x+2 and x-3 are the factors of x^3+ax+b...

hopefully it helps...... good luck mate....