According to the factor theorem, if (x-c) is a factor of f(x), then f(c)=0. Here, c=4.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the solutions to the questions:
a) Use the factor theorem to show that $(x-4)$ is a factor of $f(x) = 2x^3 - x^2 - 25x - 12$.
Step 1: According to the factor theorem, if $(x-c)$ is a factor of $f(x)$, then $f(c)=0$. Here, $c=4$.
Step 2: Substitute $x=4$ into $f(x)$:
$$f(4) = 2(4)^3 - (4)^2 - 25(4) - 12$$
$$f(4) = 2(64) - 16 - 10
