Sure, let's break down each given expression one by one and see the resulting polynomial expressions in terms of [tex]\( x \)[/tex].
### 1. [tex]\( 3x^2 + 5x \)[/tex]
This is a quadratic expression where:
- The coefficient of [tex]\( x^2 \)[/tex] is 3.
- The coefficient of [tex]\( x \)[/tex] is 5.
- There is no constant term.
So, the expression remains as:
[tex]\[ 3x^2 + 5x \][/tex]
### 2. [tex]\( 24x^2 + 16x \)[/tex]
For this quadratic expression:
- The coefficient of [tex]\( x^2 \)[/tex] is 24.
- The coefficient of [tex]\( x \)[/tex] is 16.
- There is no constant term.
So, it stays as:
[tex]\[ 24x^2 + 16x \][/tex]
### 3. [tex]\( x^2 + 5x + 6 \)[/tex]
This is a quadratic expression:
- The coefficient of [tex]\( x^2 \)[/tex] is 1.
- The coefficient of [tex]\( x \)[/tex] is 5.
- The constant term is 6.
So, the polynomial is:
[tex]\[ x^2 + 5x + 6 \][/tex]
### 4. [tex]\( x^2 - 5x + 4 \)[/tex]
Here, we have:
- The coefficient of [tex]\( x^2 \)[/tex] is 1.
- The coefficient of x is -5.
- The constant term is 4.
Thus, the expression remains:
[tex]\[ x^2 - 5x + 4 \][/tex]
### 5. [tex]\( 5 \cdot 2x^2 + 11x + 5 \)[/tex]
First, simplify the term [tex]\( 5 \cdot 2x^2 \)[/tex]:
[tex]\[ 5 \cdot 2x^2 = 10x^2 \][/tex]
So the quadratic expression becomes:
- The coefficient of [tex]\( x^2 \)[/tex] is 10.
- The coefficient of [tex]\( x \)[/tex] is 11.
- The constant term is 5.
Therefore, the final expression is:
[tex]\[ 10x^2 + 11x + 5 \][/tex]
### Summary
By examining each polynomial, we get the following set of expressions:
1. [tex]\( 3x^2 + 5x \)[/tex]
2. [tex]\( 24x^2 + 16x \)[/tex]
3. [tex]\( x^2 + 5x + 6 \)[/tex]
4. [tex]\( x^2 - 5x + 4 \)[/tex]
5. [tex]\( 10x^2 + 11x + 5 \)[/tex]
These are the step-by-step results of the given polynomial expressions.
