Answer
$3x^2 + 9x - 12$
$\text{This is a quadratic trinomial.}$
Work Step by Step
To figure the degree of a polynomial, we look at the term with the highest power.
Let us rewrite this expression in terms of descending powers; this means that we are writing the polynomial in standard form.
First, we have to expand the polynomial to get rid of the parentheses:
$3(x - 1)(x + 4)$
Multiply the first two factors, according to order of operations:
$3(x - 1)(x + 4)=(3x - 3)(x + 4)$
Multiply these two binomials using the FOIL method, meaning we multiply the first terms first, then the outer, then the inner, and, finally, the last terms:
$3(x - 1)(x + 4)=3x(x) + 3x(4) - 3(x) - (3)(4)$
$3(x - 1)(x + 4)=3x^2 + 12x - 3x - 12$
$3(x - 1)(x + 4)=3x^2 + 9x - 12$
This polynomial is now written in standard form.
In this polynomial, the term $3x^2$ has the highest power.
A second degree polynomial can be called "quadratic."
A polynomial with three terms is called a "trinomial."
There are three terms in this polynomial with the highest term being quadratic, so we call it a quadratic trinomial.
