Step 1: 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 2: Multiply the leading coefficient $\color{blue}{ a = 5 }$ by the constant term $\color{blue}{c = -26} $.
$$ a \cdot c = -130 $$Step 3: Find out two numbers that multiply to $ a \cdot c = -130 $ and add to $ b = 1 $.
Step 4: All pairs of numbers with a product of $ -130 $ are:
PRODUCT = -130 | |
-1 130 | 1 -130 |
-2 65 | 2 -65 |
-5 26 | 5 -26 |
-10 13 | 10 -13 |
Step 5: Find out which factor pair sums up to $\color{blue}{ b = 1 }$
Step 6: Because none of these pairs will give us a sum of $ \color{blue}{ 1 }$, we conclude the polynomial cannot be factored.