Factor polynomial $$ 3x^{2}+12x+15 $$

$$ 3x^{2}+12x+15 = 3( x^{2}+4x+5 ) $$

Step 1 :

After factoring out $ 3 $ we have:

$$ 3x^{2}+12x+15 = 3 ( x^{2}+4x+5 ) $$

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:

$$ \color{blue}{ b = 4 } ~ \text{ and } ~ \color{red}{ c = 5 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ 4 } $ 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}{ 4 }$, we conclude the polynomial cannot be factored.

Polynomial Factoring Calculator