Let's solve the given mathematical expressions step by step:
### Expression 1: [tex]\( a + b - c \)[/tex]
1. We are given the values:
- [tex]\( a = 2 \)[/tex]
- [tex]\( b = 3 \)[/tex]
- [tex]\( c = 4 \)[/tex]
2. Substitute these values into the expression [tex]\( a + b - c \)[/tex]:
[tex]\[
a + b - c = 2 + 3 - 4
\][/tex]
3. Perform the arithmetic operations:
[tex]\[
2 + 3 = 5
\][/tex]
[tex]\[
5 - 4 = 1
\][/tex]
So, the result of the expression [tex]\( a + b - c \)[/tex] is [tex]\( 1 \)[/tex].
### Expression 2: [tex]\( 4x^3 + 6x^2 - x - 8 \)[/tex]
1. We are given the value:
- [tex]\( x = 1 \)[/tex]
2. Substitute this value into the polynomial expression:
[tex]\[
4x^3 + 6x^2 - x - 8
\][/tex]
[tex]\[
4(1)^3 + 6(1)^2 - 1 - 8
\][/tex]
3. Compute each term individually:
[tex]\[
4(1)^3 = 4 \cdot 1 = 4
\][/tex]
[tex]\[
6(1)^2 = 6 \cdot 1 = 6
\][/tex]
[tex]\[
-x = -1
\][/tex]
[tex]\[
-8 = -8
\][/tex]
4. Combine these results:
[tex]\[
4 + 6 - 1 - 8
\][/tex]
[tex]\[
4 + 6 = 10
\][/tex]
[tex]\[
10 - 1 = 9
\][/tex]
[tex]\[
9 - 8 = 1
\][/tex]
So, the result of the polynomial [tex]\( 4x^3 + 6x^2 - x - 8 \)[/tex] when [tex]\( x = 1 \)[/tex] is [tex]\( 1 \)[/tex].
Therefore, the final answers for the given expressions are:
1. [tex]\( a + b - c \)[/tex] is [tex]\( 1 \)[/tex]
2. The polynomial [tex]\( 4x^3 + 6x^2 - x - 8 \)[/tex] evaluated at [tex]\( x = 1 \)[/tex] is [tex]\( 1 \)[/tex]
