Certainly! Let's analyze the given algebraic expression step-by-step:
Given algebraic expression:
[tex]\[
7x^4 - 3x^3 + 2x^2 + x - 9
\][/tex]
1. How many terms are in the expression?
The terms in the expression are the individual parts separated by addition or subtraction symbols. The given expression has the following terms: [tex]\( 7x^4 \)[/tex], [tex]\( -3x^3 \)[/tex], [tex]\( 2x^2 \)[/tex], [tex]\( x \)[/tex], and [tex]\( -9 \)[/tex].
- Total number of terms: [tex]\( 5 \)[/tex]
2. What is the constant term?
The constant term in an algebraic expression is the term that does not contain any variables. In this expression, the constant term is:
- Constant term: [tex]\( -9 \)[/tex]
3. What is the variable of -3?
In the expression, the coefficient of -3 is associated with the variable term [tex]\( x^3 \)[/tex].
- Variable of -3: [tex]\( x^3 \)[/tex]
4. What is the coefficient of [tex]\( x \)[/tex]?
To find the coefficient of [tex]\( x \)[/tex], we look at the term where [tex]\( x \)[/tex] appears without any exponent (other than 1). The term is [tex]\( x \)[/tex], which implies a coefficient of:
- Coefficient of [tex]\( x \)[/tex]: [tex]\( 1 \)[/tex]
5. Find the value of the expression when [tex]\( x = 2 \)[/tex].
To find the value of the expression for [tex]\( x = 2 \)[/tex], we substitute [tex]\( x \)[/tex] with 2 in the expression and then evaluate it:
[tex]\[
7(2)^4 - 3(2)^3 + 2(2)^2 + 2 - 9
\][/tex]
Evaluating step-by-step:
- [tex]\( 7(2)^4 = 7 \times 16 = 112 \)[/tex]
- [tex]\( -3(2)^3 = -3 \times 8 = -24 \)[/tex]
- [tex]\( 2(2)^2 = 2 \times 4 = 8 \)[/tex]
- [tex]\( 2 = 2 \)[/tex]
- Combining all terms: [tex]\( 112 - 24 + 8 + 2 - 9 \)[/tex]
Adding them together:
[tex]\[
112 - 24 = 88 \\
88 + 8 = 96 \\
96 + 2 = 98 \\
98 - 9 = 89 \\
\][/tex]
- Value of the expression when [tex]\( x = 2 \)[/tex]: [tex]\( 89 \)[/tex]
To summarize:
1. The number of terms is [tex]\( 5 \)[/tex].
2. The constant term is [tex]\( -9 \)[/tex].
3. The variable associated with -3 is [tex]\( x^3 \)[/tex].
4. The coefficient of [tex]\( x \)[/tex] is [tex]\( 1 \)[/tex].
5. The value of the expression when [tex]\( x = 2 \)[/tex] is [tex]\( 89 \)[/tex].
