Problem of the Week

Updated at Apr 7, 2025 11:17 AM

How would you solve \(\frac{4p{(3-p)}^{2}}{5}=\frac{16}{5}\)?

Below is the solution.



\[\frac{4p{(3-p)}^{2}}{5}=\frac{16}{5}\]

1
Multiply both sides by \(5\).
\[4p{(3-p)}^{2}=16\]

2
Expand.
\[36p-24{p}^{2}+4{p}^{3}=16\]

3
Move all terms to one side.
\[36p-24{p}^{2}+4{p}^{3}-16=0\]

4
Factor out the common term \(4\).
\[4(9p-6{p}^{2}+{p}^{3}-4)=0\]

5
Factor \(9p-6{p}^{2}+{p}^{3}-4\) using Polynomial Division.
\[4({p}^{2}-5p+4)(p-1)=0\]

6
Factor \({p}^{2}-5p+4\).
\[4(p-4)(p-1)(p-1)=0\]

7
Solve for \(p\).
\[p=4,1\]

Done
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