solve the equation 20x^3 +44x^2 -17x -5 given that -5/2 is a zero of f(x) 20x^3 +44x^2 -17x -5
I used synthetic division and got 20x^2-6x-2=0
took 2 and divided it out of that equation
2(x+5/2)=10x^2 -3x-1
then i factored it out the right side of the equation
(x+5/2)=(5x+1)(2x-1)
then i solved for x on each and got
-5/2, -1/5, 1/2
is this correct?
since x = -5/2 , one of the factors had to be (2x+5)
when you divide f(x) by 2x+5 you get
10x^2 - 3x - 1, not 20x^2 - 6x - 2
I know that when you set your answer of
20x^2 - 6x - 2 = 0 you get the same as my result when I set it mine to zero.
You have to be careful when using synthetic division by dividing polynomials by factors of the form ax ± b
it is safer to use long division for that.
you then make the statement
(x+5/2)=(5x+1)(2x-1)
that is just wrong, they are not "equal"
what you have to say is
20x^3 +44x^2 -17x -5 = 0
(2x+5)(10x^2 - 3x - 1) = 0
(2x+5)(5x+1)(2x-1) = 0
then x = -5/2 , we knew that, or
x = -1/5 or x = 1/2
I know you had those answers, but with me you would lose marks for bad form in the solution.