1. 5.6 Finding Rational Zeros Algebra II

2. The rational zero theorem…
If f(x)=anx a1x+a0 has integer coefficients, then every rational zero of f has the following form:
p factor of constant term a0
q factor of leading coefficient an n =

3. Example 1: Find rational zeros of f(x)=x3+2x2-11x-12 List possible
LC= CT=-12
X= ±1/1,± 2/1, ± 3/1, ± 4/1, ± 6/1, ±12/1
Test:
X= x=
Since -1 is a zero: (x+1)(x2+x-12)=f(x)
Factor: (x+1)(x-3)(x+4)=0
x= x=3 x=-4

4. Example 2: Find rational zeros of: f(x)=x3-4x2-11x+30 LC=1 CT=30
Test:
x= x=
X= (x-2)(x2-2x-15)=0
(x-2)(x+3)(x-5)=0
x= x= x=5

5. Ex. 3)Repeat finding zeros for:
g(x)=5x3-9x2-x+4
LC= CT=4
x:±1, ±2, ±4, ±1/5, ±2/5, ±4/5
*The graph of original shows 4/5 may be:
x=4/
(2x+3)(x-4/5)(5x2-5x-5)=
(2x+3)(x-4/5)(5)(x2-x-1)= mult.2nd factor by 5
(2x+3)(5x-4)(x2-x-1)=
-now use quad for last-
*-3/2, 4/5, 1± , 2
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6. Example 4: ____ __ f(x)=10x4-3x3-29x2+5x+12 List: LC=10 CT=12
w/ so many –sketch graph on calculator and find reasonable solutions:
x= -3/2, -3/5, 4/5, 3/2
Check:
x= -3/
Yes it works
* (x+3/2)(10x3-18x2-2x+8)*
(x+3/2)(2)(5x3-9x2-x+4) -factor out GCF
(2x+3)(5x3-9x2-x+4) multiply 1st factor by 2
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7. Assignment