Question

f(x) are given. using synthetic to write f(x) in factored form.

1. $f(x) = 4x^3 + 8x^2 - 25x - 50$; $x + 2$

Explanation:

Step1: Identify root for synthetic division

Root from $x+2$ is $x=-2$.

Step2: Set up synthetic division

Write coefficients: $4, 8, -25, -50$; use root $-2$.

$$\begin{array}{r|rrrr} -2 & 4 & 8 & -25 & -50 \\ \hline & & -8 & 0 & 50 \\ \hline & 4 & 0 & -25 & 0 \end{array}$$

Step3: Get quadratic factor

Resulting quadratic: $4x^2 -25$.

Step4: Factor quadratic

Factor as difference of squares: $4x^2-25=(2x-5)(2x+5)$.

Step5: Combine all factors

Include given factor $(x+2)$.

Answer:

$f(x)=(x+2)(2x-5)(2x+5)$