To solve the given quadratic expression [tex]\(4x^2 + 7x + 3\)[/tex], let's break it down and understand each term in detail.
### Step-by-Step Solution:
1. Identify the quadratic expression:
The expression is [tex]\(4x^2 + 7x + 3\)[/tex].
2. Understand each term:
- The term [tex]\(4x^2\)[/tex] is the quadratic term (the term with [tex]\(x\)[/tex] raised to the power of 2).
- The term [tex]\(7x\)[/tex] is the linear term (the term with [tex]\(x\)[/tex] raised to the power of 1).
- The term [tex]\(3\)[/tex] is the constant term (the term without [tex]\(x\)[/tex]).
3. Write down the expression in its standard form:
A quadratic expression is typically written in the form [tex]\(ax^2 + bx + c\)[/tex]:
- Here, [tex]\(a = 4\)[/tex], [tex]\(b = 7\)[/tex], and [tex]\(c = 3\)[/tex].
4. Expand the expression:
In this case, the expression [tex]\(4x^2 + 7x + 3\)[/tex] is already in its expanded form. The expanded form of a polynomial is the expression written out with all the terms laid out explicitly, which we already have.
So, the expression [tex]\(4x^2 + 7x + 3\)[/tex] is fully expanded, and we can write the solution simply as:
[tex]\[ 4x^2 + 7x + 3 \][/tex]
This quadratic expression doesn't require any further simplification. It is already in its simplest and expanded form.
