Urgent Polynomial Help (1 Viewer)

[M@ster P]

The remainder, when f(x) = ax^4 + bx^3 + 15x^2 + 9x + 2 is divided by x - 2 is 216 and x +1 is a factor of f(x). Find a and b.

The answer i got was a = 13 and b = -9, but the answer in the text book was a = 3 and b = 11.

Thx guys

 

[charisloke]

I got a = 3 and b = 11.
For the first one, substitute 2 in for x:
216 = 16a + 8b + 60 + 18 + 2
216 = 80 + 16a + 8b
27 = 10 + 2a + b (1)
And the next one, -1 for x:
0 = a - b + 8 (2)
So through simultaneous equation,
Eq (1) + Eq (2) gives 27=18 + 3a
a=3 and b=11

 

[M@ster P]

i realise my mistake now, at the step 216 = 80 + 16a + 8b, I subtracted 80 from 216 leaving me an answer of 136, when in your solution you left the step as it was and simplified it.

 

[M@ster P]

thx charisloke