Question

if (x+1) and (x-1) are factors of ax³+x²-2x+b,find the value of a and b.also find third factor

Answer 1

hope this answer helps

Answer 2

(x-1) and (x+1) are factors of the given polynomial.

(x-1) = 0 → x=1

(x+1) = 0 → x= -1

Put x = 1

ax³+x²-2x+b

a(1)³+(1)²-2(1)+b = 0

a(1)+1-2+b = 0

a-1+b = 0

a+b = 1 -----(1)

Put x = -1

a(-1)³+(-1)²-2(-1)+b = 0

a(-1)+1+2+b = 0

-a+3+b = 0

-a+b = -3 -----(2)

(1)+(2)

a+b = 1
-a+b = -3
-------------

2b = -2

b = -2/2 = -1

a+b = 1

a+(-1) = 1

a = 1+1

a = 2

Therefore,a = 2 and b = -1

The given polynomial is

2x³+x²-2x+(-1)

2x³+x²-2x-1

Let the third zero be 'q'

Sum of zeroes = -1+1+p = p = -coefficient of x²/coefficient of x³

p = -1/2

Therefore, the third factor = (x+1/2)

Hope it helps