Factor polynomial $$ 6x^{3}+x^{2}-35x $$

$$ 6x^{3}+x^{2}-35x = x( 3x-7 )( 2x+5 ) $$

Step 1 :

After factoring out $ x $ we have:

$$ 6x^{3}+x^{2}-35x = x ( 6x^{2}+x-35 ) $$

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:

$$ a = 6 , b = 1 ~ \text{ and } ~ c = -35 $$

Step 3: Multiply the leading coefficient $\color{blue}{ a = 6 }$ by the constant term $\color{blue}{c = -35} $.

$$ a \cdot c = -210 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = -210 $ and add to $ b = 1 $.

Step 5: All pairs of numbers with a product of $ -210 $ are:

PRODUCT = -210
-1     210	1     -210
-2     105	2     -105
-3     70	3     -70
-5     42	5     -42
-6     35	6     -35
-7     30	7     -30
-10     21	10     -21
-14     15	14     -15

Step 6: Find out which factor pair sums up to $\color{blue}{ b = 1 }$

PRODUCT = -210 and SUM = 1
-1     210	1     -210
-2     105	2     -105
-3     70	3     -70
-5     42	5     -42
-6     35	6     -35
-7     30	7     -30
-10     21	10     -21
-14     15	14     -15

Step 7: Replace middle term $ 1 x $ with $ 15x-14x $:

$$ 6x^{2}+x-35 = 6x^{2}+15x-14x-35 $$

Step 8: Apply factoring by grouping. Factor $ 3x $ out of the first two terms and $ -7 $ out of the last two terms.

$$ 6x^{2}+15x-14x-35 = 3x\left(2x+5\right) -7\left(2x+5\right) = \left(3x-7\right) \left(2x+5\right) $$

Polynomial Factoring Calculator