Question

Solve the polynomial equation x^3 - 5x^2 + x when x = 4

Answer 1

To solve the polynomial equation \( x^3 - 5x^2 + x \) when \( x = 4 \), we can substitute \( 4 \) into the equation:

\[
x^3 - 5x^2 + x = 4^3 - 5(4^2) + 4
\]

Calculating each term:

1. \( 4^3 = 64 \)
2. \( 5(4^2) = 5 \times 16 = 80 \)
3. The last term is simply \( 4 \).

Now, substituting these values back into the equation:

\[
64 - 80 + 4
\]

Now, performing the arithmetic:

\[
64 - 80 = -16
\]
\[
-16 + 4 = -12
\]

Thus, the value of the polynomial \( x^3 - 5x^2 + x \) when \( x = 4 \) is \( -12 \).