synthetic division yields remainders
f(x) = (x-2)*p(x) + 8a+2b-28
f(x) = (x+4)*q(x) + (-64a-4b-40)
so,
8a+2b = 28
64a+4b = -40
a = -2
b = 22
f(x) = (x-2)(x+4)(-2x+3)
The function f(x)=ax^3-x^3+bx-24 has three factors. Two of these factors are x-2 and x+4. Determine the values of a and b , and then determine the other factor
2 answers
If you are confused about how they jump from two equations to the answers, I'll simplify your studying in three words - Method of Elimination. You may remember it from solving linear problems in earlier years, anyway I'll explain it briefly as a refresher but it might be easier if you watch a tutorial on it. The Method of Elimination basically means to "eliminate" a variable. Take the two equations that we found by factoring
1. 8a+2b=28
2. -64a-4b=40
We need to eliminate one of them, the easiest one to zero out is b, we can do that by multiplying equation 1 by 2. See below:
8a+2b=28 X2 = 16a +4b=56
Now plain and simple add the new equation 1 to the original equation 2.
(16a +4b=56) + (-64a-4b=40) = -48a +0b = 96 or -48a=96
Solve for a which gives you -2 and then use the a value to solve for b.
1. 8a+2b=28
2. -64a-4b=40
We need to eliminate one of them, the easiest one to zero out is b, we can do that by multiplying equation 1 by 2. See below:
8a+2b=28 X2 = 16a +4b=56
Now plain and simple add the new equation 1 to the original equation 2.
(16a +4b=56) + (-64a-4b=40) = -48a +0b = 96 or -48a=96
Solve for a which gives you -2 and then use the a value to solve for b.
2 answers