factor completely. If the polynomial is not factorable, write “prime.” 48-20x+2x^2

Question

please show steps

Answer 1

Let's rearrange terms in descending order of exponents and factor out 2, obtaining the equivalent expression

2(x² -10x +24) and then we'll get 2(x-4)(x-6).

 

Note how, when FOILing to check, the product of those two binomials produces CONSTANT +24 and middle term -10x.  

That's why we don't factor +24 as (-3)(-8) because we'd get -11x as the (erroneous) middle term.