SOLUTION: f(x) = 2x^3 + 11x^2 - 21x - 90. (10) a. Use the rational zero test to list all possible rational zeros of f. I found these to be x= 3,-5/2,-6 b. Write f as a product of line

Question 1183005: f(x) = 2x^3 + 11x^2 - 21x - 90. (10)
a. Use the rational zero test to list all possible rational zeros of f.
I found these to be x= 3,-5/2,-6
b. Write f as a product of linear factors algebraically. Show all your work
including synthetic division.
Found 3 solutions by ikleyn, josgarithmetic, MathTherapy:
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

You correctly determined the roots.

I have checked it by direct substitution and calculation.

As soon as you know all the roots, you can write the linear decomposition as

            f(x) = 2*(x-3)*(x+5/2)*(x+6) = (x-3)*(2x+5)*(x+6).             ANSWER

Solved.

Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
90 is 2*3*3*5.

To find all possible roots according to the theorem,

Plus and minus of :
90/2, 45/2, 18/2, 15/2, 10/2, 9/2, 5/2, 3/2, 2/2, 6/2
which are
45, 45/2, 9, 15/2, 5, 9/2, 5/2, 3/2, 1/2, 3

and the plus and minus of :
90, 45, 18, 15, 10, 9, 5, 3, 2, 1, 6
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
f(x) = 2x^3 + 11x^2 - 21x - 90. (10)
a. Use the rational zero test to list all possible rational zeros of f.
I found these to be x= 3,-5/2,-6
b. Write f as a product of linear factors algebraically. Show all your work
including synthetic division.

All POSSIBLE rational zeros of f: ====>
That's a total of 48 POSSIBLE ZEROES, but with some factors being duplicates , the number of zeroes decreases.
Now, which ones prove to be ACTUAL ZEROES, you've already determined that.
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