Step 1 :
After factoring out $ -1 $ we have:
$$ -5x^{2}+6x+8 = - ~ ( 5x^{2}-6x-8 ) $$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:
Step 3: Multiply the leading coefficient $\color{blue}{ a = 5 }$ by the constant term $\color{blue}{c = -8} $.
$$ a \cdot c = -40 $$Step 4: Find out two numbers that multiply to $ a \cdot c = -40 $ and add to $ b = -6 $.
Step 5: All pairs of numbers with a product of $ -40 $ are:
PRODUCT = -40 | |
-1 40 | 1 -40 |
-2 20 | 2 -20 |
-4 10 | 4 -10 |
-5 8 | 5 -8 |
Step 6: Find out which factor pair sums up to $\color{blue}{ b = -6 }$
PRODUCT = -40 and SUM = -6 | |
-1 40 | 1 -40 |
-2 20 | 2 -20 |
-4 10 | 4 -10 |
-5 8 | 5 -8 |
Step 7: Replace middle term $ -6 x $ with $ 4x-10x $:
$$ 5x^{2}-6x-8 = 5x^{2}+4x-10x-8 $$Step 8: Apply factoring by grouping. Factor $ x $ out of the first two terms and $ -2 $ out of the last two terms.
$$ 5x^{2}+4x-10x-8 = x\left(5x+4\right) -2\left(5x+4\right) = \left(x-2\right) \left(5x+4\right) $$