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

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) (Show Source): You can put this solution on YOUR website!
Solve for x: f(x)=2x^3+3x^2-8x+3=0
----------
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
===================================
Cheers,
Stan H.

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