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Question

Factor the polynomial completely.

30x⁴−38x³+12x²

Answer 1

Hi Candice,

 

 

   Factor the polynomial completely.
30x⁴−38x³+12x²

 

First we ask:  Is there a greatest common factor (GCF) that can be factored out of the trinomial expression?

 

YES.   The coefficients are 30, -38 and 12. The GCF is 2.

So far we have:   2(15x⁴−19x³+6x²)

 

Next we ask:  What is the greatest number of x's that can be factored out?  2 x's

When factoring out exponents, subtract the exponents.

2x²(15x²−19x+6)

Are we finished yet?  No

Can the trinomial be factored?  Yes

How?  There is a process called the "Double Slide" which works wonderfully. 

I'll explain.

 

The trinomial:            15x²−19x+6

Multiply the coefficient of the 1st term times the last term:  x²-19x+6(15)

Now we have:   x²-19x+90

Since the last term is positive, both factors must be the same sign.

Since the 2nd term is negative, both factors must be negative.

So we need factors of 90 which add up to -19

-1   -90  no

-2   -45  no

-3   -30  no

-5    -18  no but we are getting closer

-6    -15  not yet

-9    -10   finally!   -9+-10=-19

 

  The factors are:   (x-9)(x-10)     

 BUT since we multiplied by 15 in the beginning, now we have to divide each factor by 15

 

              (x-9/15)(x-10/15)    

 

Reduce:   (x-3/5)(x-2/3)   

Since the fractions are fully reduced, slide the denominators in front of the x variable in each factor  

   

(x-3/5)(x-2/3)

(5x-3)(3x-2)

 

The last step is to add the GFC we found before to both the factors:

 

2x²(5x-3)(3x-2)   That's the answer.

 

Hope this helps you out with the process.

                        

Answer 2

Factor out 2x^2 from the equation 

 

2x^2 ( 15x^2 - 19x + 6 )

 

 

2x^2 (5x - 3) (3x - 2)

 

I hope this helped you out Candace.