Answer
$f(x)=(2x-1)(3x-2)(5x+7)$
Work Step by Step
In part b) we wrote the polynomial in the form:
$$f(x)=\left(x-\dfrac{1}{2}\right)(30x^2+22x-28).$$
We have to factor $f$ completely:
$$\begin{align*}
f(x)&=2\left(x-\dfrac{1}{2}\right)(15x^2+11x-14)\\
&=2\left(x-\dfrac{1}{2}\right)((15x^2-10x)+(21x-14))\\
&=2\left(x-\dfrac{1}{2}\right)(5x(3x-2)+7(3x-2))\\
&=2\left(x-\dfrac{1}{2}\right)(3x-2)(5x+7)\\
&=(2x-1)(3x-2)(5x+7).
\end{align*}$$
Therefore we got the linear decomposition:
$$f(x)=(2x-1)(3x-2)(5x+7).$$
