Sure, let's solve the expression \(5x^3 + x^2 - 10x\) for \(x = 2\) step by step.
1. Substitute \(x = 2\) into the expression:
[tex]\[
5(2)^3 + (2)^2 - 10(2)
\][/tex]
2. Calculate each term individually:
- First term: \(5(2)^3\)
[tex]\[
(2)^3 = 2 \times 2 \times 2 = 8
\][/tex]
[tex]\[
5 \times 8 = 40
\][/tex]
- Second term: \((2)^2\)
[tex]\[
(2)^2 = 2 \times 2 = 4
\][/tex]
- Third term: \(-10(2)\)
[tex]\[
-10 \times 2 = -20
\][/tex]
3. Combine the calculated terms:
[tex]\[
40 + 4 - 20
\][/tex]
4. Perform the addition and subtraction:
[tex]\[
40 + 4 = 44
\][/tex]
[tex]\[
44 - 20 = 24
\][/tex]
The value of the expression [tex]\(5x^3 + x^2 - 10x\)[/tex] when [tex]\(x = 2\)[/tex] is [tex]\(\boxed{24}\)[/tex].
