Question

11.) SOLVE the equation for w by using "factoring by grouping". YOUMUST SHOW ALL STEPS of the grouping process, especially theFIRST STEP of grouping to receive FULL CREDIT. (10 pts)2w3 + 5w2 - 32w - 80 = 0

Answer 1

w = -5/2, w = 4 and w = -4

Explanation:

We have the following equiation:

`2w^3+5w^2-32w-80=0`

We solve with the help of factoring by grouping

`\begin{gathered} (2w^3+5w^2)+(-32w-80)=0 \\ w^2\cdot(2w+5)-16\cdot(2w+5)=0 \\ (2w+5)\cdot(w^2-16)=0 \\ 2w+5=0\rightarrow w=-(5)/(2) \\ (w^2-16)=0\rightarrow w^2=16\rightarrow w=\pm4\rightarrow w=4,w=-4 \end{gathered}`

The solutions are w = -5/2, w = 4 and w = -4