SOLUTION: I need help with this: find the polynomial written as a product of linear factors: f(x)=2x^3+5x^2-11x+4

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I need help with this: find the polynomial written as a product of linear factors: f(x)=2x^3+5x^2-11x+4      Log On


   

Question 86378: I need help with this: find the polynomial written as a product of linear factors: f(x)=2x^3+5x^2-11x+4
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
find the polynomial written as a product of linear factors: f(x)=2x^3+5x^2-11x+4
--------
Because the coefficients add up to zero, x=1 is a root; so (x-1) is a factor.
Using synthetic division you get:
1)2....5....-11....4
....2....7.....-4..|..0
=========
Remainder = 0
Quotient = 2x^2+7x-4
Factor the quotient:
2x^2-8x+x-4
2x(x-4)+(x-4)
(x-4)(2x+1)
===============
Therefore f(x) = (x-1)(x-4)(2x+1)
==============
Cheers,
Stan H.