SOLUTION: If (2x-1) is a factor of f(x)=2x^3-5x^2-kx+3 find the value of k. Find the other two factors of f(x)=0

Algebra.Com
Question 366845: If (2x-1) is a factor of f(x)=2x^3-5x^2-kx+3 find the value of k.
Find the other two factors of f(x)=0

Answer by Jk22(389)   (Show Source): You can put this solution on YOUR website!
Dividing the polynomials gives :

2x^3 - 5x^2 - kx + 3 | 2x - 1
------------------------------
2x^3 - x^2............| x^2 - 2x - (k+2)/2
----------------------|
-4x^2 - kx + 3........|
-4x^2 + 2x............|
----------------------|
-(k+2)x + 3...........|
-(k+2)x + (k+2)/2.....|
----------------------|
3 - (k+2)/2


the remainder should equals zero, hence k+2 = 6, k = 4

we can check another way by the fact the 1/2 has to be a solution :

2/8 - 5/4 - 2 + 3 = 1/4 - 5/4 + 1 = -4/4 + 1 = 0


the remaining polynomial is : x^2 - 2x - 3 = (x-3)(x+1) by Viete's formula.


the 2 other roots are : 3 and -1


check : for x=3 : 2*27 - 5*9 - 4*3 + 3 = 54 - 45 - 12 + 3 = 9 - 12 + 3 = 0

x=-1 : -2 - 5 + 4 + 3 = -7 + 7 = 0

RELATED QUESTIONS

If (2x-1) is a factor of f(x)=2x^3-5x^2-kx+3 find the value of k. Find the other two... (answered by stanbon)
the binomial (x+4) is a factor of the following polynomials, find the value of k.... (answered by ikleyn,MathTherapy)
Determine the value of k in f(x)=2x^3+kx^2-28x-15 such that x-3 is a factor. (answered by josgarithmetic)
if x+1 is a factor of x^3+3x^2+kx+4, find the value of... (answered by Boreal,ikleyn)
If x+2 is a factor of 2x^3+kx^2+16x, what is the value of... (answered by htmentor)
Find the value of k such that x-2 is a factor of kx^3 - kx^2 + x+2 (answered by ikleyn)
Given f(x)=x^3+kx+2, and x+1 is a factor of f(x), then what is the value of... (answered by Edwin McCravy,ikleyn)
Find k so that the minimum value of f(x) =x^2 +kx+8 is equal to the maximum value of g(x) (answered by stanbon)
Find k so that the minimum value of f(x) = x^2 + kx + 8 is equal to the maximum value of... (answered by ikleyn,Solver92311)