You can put this solution on YOUR website! If x-2 is a factor of P(x) = ax^3 +bx^2 - 5x + 6 and P(-1)=6, find a and b.
:
using the form:
ax^3 + bx^2 - 5x + 6 = y
:
Write an equation for factor; (x-2)
x=2; y=0
8a + 4b - 5(2) + 6 = 0
8a + 4b - 10 + 6 = 0
8a + 4b - 4 = 0
8a + 4b = 4
simplify, divide by 4
2a + b = 1
:
P(-1)=6
x=-1; y=6
-1a + 1b - 5(-1) + 6 = 6
-1a + 1b + 5 + 6 = 6
-a + b + 11 = 6
-a + b = 6 - 11
-a + b = -5
:
Use elimination on these 2 equations
2a + b = 1
-a + b = -5
---------------Subtraction eliminates b, find a
3a + 0 = 6
a = 6/3
a = 2
Find a using -a + b = -5
-2 + b = -5
b = - 5 + 2
b = -3
:
This makes our equation: p(x) = 2x^3 - 3x^2 - 5x + 6; a=2; b=-3
looks like this
