Factor polynomial $$ 10x^{2}-32x+24 $$

$$ 10x^{2}-32x+24 = 2( x-2 )( 5x-6 ) $$

Step 1 :

After factoring out $ 2 $ we have:

$$ 10x^{2}-32x+24 = 2 ( 5x^{2}-16x+12 ) $$

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:

$$ a = 5 , b = -16 ~ \text{ and } ~ c = 12 $$

Step 3: Multiply the leading coefficient $\color{blue}{ a = 5 }$ by the constant term $\color{blue}{c = 12} $.

$$ a \cdot c = 60 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = 60 $ and add to $ b = -16 $.

Step 5: All pairs of numbers with a product of $ 60 $ are:

PRODUCT = 60
1     60	-1     -60
2     30	-2     -30
3     20	-3     -20
4     15	-4     -15
5     12	-5     -12
6     10	-6     -10

Step 6: Find out which factor pair sums up to $\color{blue}{ b = -16 }$

PRODUCT = 60 and SUM = -16
1     60	-1     -60
2     30	-2     -30
3     20	-3     -20
4     15	-4     -15
5     12	-5     -12
6     10	-6     -10

Step 7: Replace middle term $ -16 x $ with $ -6x-10x $:

$$ 5x^{2}-16x+12 = 5x^{2}-6x-10x+12 $$

Step 8: Apply factoring by grouping. Factor $ x $ out of the first two terms and $ -2 $ out of the last two terms.

$$ 5x^{2}-6x-10x+12 = x\left(5x-6\right) -2\left(5x-6\right) = \left(x-2\right) \left(5x-6\right) $$

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