Factor polynomial $$ 36t^{4}-144t^{3}+288t^{2} $$

$$ 36t^{4}-144t^{3}+288t^{2} = 36t^{2}( t^{2}-4t+8 ) $$

Step 1 :

After factoring out $ 36t^{2} $ we have:

$$ 36t^{4}-144t^{3}+288t^{2} = 36t^{2} ( t^{2}-4t+8 ) $$

Step 2 :

Step 2: Identify constants $ \color{blue}{ b }$ and $\color{red}{ c }$. ( $ \color{blue}{ b }$ is a number in front of the $ x $ term and $ \color{red}{ c } $ is a constant). In our case:

$$ \color{blue}{ b = -4 } ~ \text{ and } ~ \color{red}{ c = 8 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ -4 } $ and multiply to $ \color{red}{ 8 } $.

Step 3: Find out pairs of numbers with a product of $\color{red}{ c = 8 }$.

PRODUCT = 8
1     8	-1     -8
2     4	-2     -4

Step 4: Because none of these pairs will give us a sum of $ \color{blue}{ -4 }$, we conclude the polynomial cannot be factored.

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