Factor polynomial $$ -4a^{6}+8a^{5}-2a^{4} $$

$$ -4a^{6}+8a^{5}-2a^{4} = ( -2 )a^{4}( 2a^{2}-4a+1 ) $$

Step 1 :

After factoring out $ -2a^{4} $ we have:

$$ -4a^{6}+8a^{5}-2a^{4} = -2a^{4} ( 2a^{2}-4a+1 ) $$

Step 2 :

Step 2: Identify constants $ a $ , $ b $ and $ c $.
$ a $ is a number in front of the $ x^2 $ term $ b $ is a number in front of the $ x $ term and $ c $ is a constant. In this case:

$$ a = 2 , b = -4 ~ \text{ and } ~ c = 1 $$

Step 3: Multiply the leading coefficient $\color{blue}{ a = 2 }$ by the constant term $\color{blue}{c = 1} $.

$$ a \cdot c = 2 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = 2 $ and add to $ b = -4 $.

Step 5: All pairs of numbers with a product of $ 2 $ are:

PRODUCT = 2
1     2	-1     -2

Step 6: Find out which factor pair sums up to $\color{blue}{ b = -4 }$

Step 7: Because none of these pairs will give us a sum of $ \color{blue}{ -4 }$, we conclude the polynomial cannot be factored.

Polynomial Factoring Calculator