How to do division pf polynomials

Question

Dividing polynomials by binomial and trinomial, I am very new to algebra and we are in intermediate algebra, they just gave me the class, I'm an online student (67yrs of age), never ever had this before and I am failing the class.

16 to the power of 2 -56x + 40 divided by 8.  I studied the samples, but I am lost.

Answer 1

Admire your pluck for attacking math.  First for some nomenclature.  16 to the power of two is better written 16² or 16^2 where the caret is understood to elevate the argument to the designated exponent.

(16x^2   -   56x   +   40)/8 

Divide each term in the numerator (top) by 8.

=(2x^2   -   7x   +   5)

Your introduction mentioning binomials & trinomials made me put x^2 in. 

If there is no x^2 following 16, the expression becomes (16^2   -56x   +40)/8   =   (16*16  +   40   -   56x)/8   =   

(16*2   +   5    -7x) =  (37   -   7x)