Originally Posted by
Mr Rayon The remainder when x^3 + ax^2 + bx + 1 is divided by (x - 5) is -14. When the cubic polynomial is divided by (x + 1), the remainder is -2. Find a and b.
To solve a and b, I did the following:
P(5) = 5^3 + a(5)^2 + b(5) + 1
= 125 + 25a + 5b + 1
= 25a + 5b + 126
25a + 5b + 126 = -14
P(-1) = (-1)^3 + a(-1)^2 + b(-1) + 1
= -1 + a - b + 1
= a - b
a - b = -2
Using the method of elimination:
25a + 5b = -140
25a - 25b = -50
30b = -190 Mr F says: -140 - (-50) = -90. So you should have 30b = -90.
b= -19/3
Substituting the value of b into: a - b = -2
a - (-19/3) = -2
a + 19/3 = -2
a = -25/3
But the answers are supposed to be:
a = -5, b= -3
What did I do wrong? Please show me complete working out. All help will be appreciated.