Factor polynomial $$ -3x^{4}-9x^{3}+15x^{2} $$

$$ -3x^{4}-9x^{3}+15x^{2} = ( -3 )x^{2}( x^{2}+3x-5 ) $$

Step 1 :

After factoring out $ -3x^{2} $ we have:

$$ -3x^{4}-9x^{3}+15x^{2} = -3x^{2} ( x^{2}+3x-5 ) $$

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:

$$ \color{blue}{ b = 3 } ~ \text{ and } ~ \color{red}{ c = -5 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ 3 } $ and multiply to $ \color{red}{ -5 } $.

Step 3: Find out pairs of numbers with a product of $\color{red}{ c = -5 }$.

PRODUCT = -5
-1     5	1     -5

Step 4: Because none of these pairs will give us a sum of $ \color{blue}{ 3 }$, we conclude the polynomial cannot be factored.

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