Question

if the polynomial x3+2x2+ax+b has factor x+1 and x-1 find the value of a and b

Answer 1

Heya mate ur answer
_________________

x-1 and x+1 are factors of polynomial
x-1=0 and x+1 =0
x=1 and x=-1 are zeros of this polynomial

Put both values of x in the polynomial.
____________________

P(1)= 1^3+2(1)^2+a(1) +b=0
1+2+a+b=0
3+a+b=0
a+b= -3
a= -3-b ------ equation 1
___________________

P(-1) =(-1)^3+2(-1)^2+a(-1)+b=0
-1+2-a+b=0
1-a+b=0
-a+b=1
b= 1+a ------ equation 2
Put the value of b in equation 1

a= -3-(1+a)
a= -3-1-a
a= -4-a
a+a= -4
2a= -4
a= -4/2
a= -2
Put the value of a in equation 2

b= 1+(-2)
b= 1-2
b= -1

Therefore the value of a is -2 and value of b is -1
Hope it helps......
^_^ ^_^

Answer 2

Step-by-step explanation:

x-1 and x+1 are factors of polynomial

x-1=0 and x+1 =0

x=1 and x=-1 are zeros of this polynomial

Put both values of x in the polynomial.

____________________

P(1)= 1^3+2(1)^2+a(1) +b=0

1+2+a+b=0

3+a+b=0

a+b= -3

a= -3-b ------ equation 1

___________________

P(-1) =(-1)^3+2(-1)^2+a(-1)+b=0

-1+2-a+b=0

1-a+b=0

-a+b=1

b= 1+a ------ equation 2

Put the value of b in equation 1

a= -3-(1+a)

a= -3-1-a

a= -4-a

a+a= -4

2a= -4

a= -4/2

a= -2

Put the value of a in equation 2

b= 1+(-2)

b= 1-2

b= -1

Therefore the value of a is -2 and value of b is -1