Factor completely. If Polynomial is prime , state this.

Question

Factor completely. If Polynomial is prime , state this.

-20+31x-12x^2

Answer 1

The best way to factor is to change all the signs of the terms in the expression using distributive property. Lets say that -1 is a common factor of the terms.

 

- (20 - 31x + 12x²)

 

 

Now we can easily try to factor the term in parenthesis using FOIL since the coefficient of x² is positive.

 

- [(5 - 4x)(4 - 3x)]

 

 

This cannot be factored any further.  Therefore, you have

 

- (5 - 4x)(4 - 3x)

Answer 2

-12x²+31x-20 = -(12x²-31x+20) = -12(x-4/3)(x-5/4)  ... I obtained these roots using quadratic formula ...

 

= -(3x-4)(4x-5)   ...last step here is corrected.