The "standard form" of a polynomial refers to its order. In standard form, terms are listed in order of descending degree.
Degree refers to the sum of the exponents in a single term. For example, the degree of #12x^5# is #5#, since that is its only exponent. The degree of #-3x^2y# is #3# because the #x# is raised to the #2# and the #y# is raised to the #1#, and #2+1=3#. Any constant, like #11#, has a degree of #0# because it can technically be written as #11x^0# since #x^0=1#.
In #(x+5)(4x+7)#, we first have to distribute all of the terms. This leaves us with #4x^2+7x+20x+35#, which simplifies to be #4x^2+27x+35#.
Now, all we have to do is make sure we are in standard form. The degrees, as they are currently listed, go in the order #2rarr1rarr0#, which is in descending order. Therefore, the polynomial in standard form is #color(red)(4x^2+27x+35#
