SOLUTION: Solve for x: f(x)=2x^3+3x^2-8x+3=0 How can I find all possible roots and for this polynomial. How can I sketch a graph of this? My instructor also uses synthetic divsion after h

Algebra ->  Rational-functions -> SOLUTION: Solve for x: f(x)=2x^3+3x^2-8x+3=0 How can I find all possible roots and for this polynomial. How can I sketch a graph of this? My instructor also uses synthetic divsion after h      Log On


   

Question 137150This question is from textbook College Algebra
: Solve for x: f(x)=2x^3+3x^2-8x+3=0
How can I find all possible roots and for this polynomial. How can I sketch a graph of this?
My instructor also uses synthetic divsion after he finds the first root and factor. This question is from textbook College Algebra

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x: f(x)=2x^3+3x^2-8x+3=0
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Notice that f(1) = 2+3-8+3 =0
That means 1 is a zero; use it with synthetic division to find the quotient:
1)....2....3....-8....3
.......2....5.....-3..|..0
Quotient: 2x^2+5x-3
Factor with AC Method:
2x^2+6x-x-3
2x(x+3-(x+3)
= (x+3)(2x-1)
x = 1, or x = -3 or x = 1/2
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Cheers,
Stan H.