SOLUTION: If anyone can show the steps to solve this problem/problem like this, I would really appreciate it. I cannot find a video or example problem from my course on how to solve this.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: If anyone can show the steps to solve this problem/problem like this, I would really appreciate it. I cannot find a video or example problem from my course on how to solve this.       Log On


   



Question 1176560: If anyone can show the steps to solve this problem/problem like this, I would really appreciate it. I cannot find a video or example problem from my course on how to solve this.

Given the function f(x) = 4x^3 + 19x^2 − 8x − 15, and knowing one factor is (x + 5), write f(x)as a product of linear factors without fractions.
f(x) =

Found 3 solutions by ikleyn, josgarithmetic, ewatrrr:
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.

I can instruct you immediately, without the reference to a video lesson.

    1.  Under given info, simply divide the given polynomial of the degree 3 by the binomial (x+5), using long division, for example.



    2.  You will get the quadratic polynomial as a quotient.


        Find the roots of this quadratic polynomial.


        The associated linear binomials will be the factors of your given polynomial of the degree 3.

That's all.


/\/\/\/\/\/\/\/

The post by @josgarithmetic is  INCORRECT.

THEREFORE,  for your safety,  simply  IGNORE  it.



        *************************************************************************

                When you obtain  "solutions"  from @josgarithmetic,  REMEMBER  that
                half of his posts are  INCORRECT - it is the usual style of his work.

        *************************************************************************



Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
You could try factoring, or try applying Rational Roots Theorem, or attempt long division or synthetic division starting with x%2B5 as divisor.
-5  |   4   19   -8   -15
    |      -20    5   15
    |------------------------
        4   -1    -3


1   |   4   -1    -3
    |      4      3
    |_________________
        4   3     0--------------meaning, facto4x%2B3

Roots are -5, 1, and -3/4.
f%28x%29=%28x%2B5%29%28x-1%29%284x%2B3%29





------------------This contains an early arithmetic mistake and is wrong-----------------
%284x%5E3%2B19x%5E2-8x-15%29%2F%28x%2B5%29
-5   |    4    19     -8    -15
     |
     |        -20     -5    115
     |__________________________________
         4      1    -23    100

This means f%28x%29=cross%28%28x%2B5%29%284x%5E2%2Bx-23%2B100%2F%28x%2B5%29%29%29 .


Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!

Synthetic Division:
-5	4	19	-8	-15
		-20	5	+15
	4	-1	-3	  0

ie:  (x+5)(4x^2 - x - 3) = 0
     (x+5)(4x +3 )(x - 1) = 0