If the polynomial ax3 + bx2 - c is divisible by x2 + bx +c then what is the value of 'ab'?
Answer: If the polynomial ax3 + bx2 - c is divisible by x2 + bx + c then value of ab is 1.
As ax3 + bx2 - c is divisible by x2 + bx +c, then the remainder is 0.
The remainder when ax3 + bx2 - c is divided by x2 + bx +c is 0.
Let f(x) = ax3 + bx2 - c and g(x) = x2 + bx + c
Now, dividing f(x) by g(x) we get, (ax3 +bx2 - c) / (x2 + bx + c)
Use the Cuemath's long division of polynomial calculator, to find the quotient and the remainder.
We see that the quotient comes to be (ax - ab) and the remainder = (ab² – ac + b) x + c (ab – 1)
Now as the remainder is 0 and the value of x and c is not equal to 0.
Therefore, ab² – ac + b = 0 and ab – 1 = 0
==> ab = 1