Factor polynomial $$ -8m^{2}-56m-98 $$

$$ -8m^{2}-56m-98 = ( -2 )( 2m+7 )^{ 2 } $$

Step 1 :

After factoring out $ -2 $ we have:

$$ -8m^{2}-56m-98 = -2 ( 4m^{2}+28m+49 ) $$

Step 2 :

Both the first and third terms are perfect squares.

$$ 4x^2 = \left( \color{blue}{ 2m } \right)^2 ~~ \text{and} ~~ 49 = \left( \color{red}{ 7 } \right)^2 $$

The middle term ( $ 28x $ ) is two times the product of the terms that are squared.

$$ 28x = 2 \cdot \color{blue}{2m} \cdot \color{red}{7} $$

We can conclude that the polynomial $ 4m^{2}+28m+49 $ is a perfect square trinomial, so we will use the formula below.

$$ A^2 + 2AB + B^2 = (A + B)^2 $$

In this example we have $ \color{blue}{ A = 2m } $ and $ \color{red}{ B = 7 } $ so,

$$ 4m^{2}+28m+49 = ( \color{blue}{ 2m } + \color{red}{ 7 } )^2 $$

Polynomial Factoring Calculator