Factor polynomial $$ -8x^{2}+10x-3 $$

$$ -8x^{2}+10x-3 = -( 4x-3 )( 2x-1 ) $$

Step 1 :

After factoring out $ -1 $ we have:

$$ -8x^{2}+10x-3 = - ~ ( 8x^{2}-10x+3 ) $$

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:

$$ a = 8 , b = -10 ~ \text{ and } ~ c = 3 $$

Step 3: Multiply the leading coefficient $\color{blue}{ a = 8 }$ by the constant term $\color{blue}{c = 3} $.

$$ a \cdot c = 24 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = 24 $ and add to $ b = -10 $.

Step 5: All pairs of numbers with a product of $ 24 $ are:

PRODUCT = 24
1     24	-1     -24
2     12	-2     -12
3     8	-3     -8
4     6	-4     -6

Step 6: Find out which factor pair sums up to $\color{blue}{ b = -10 }$

PRODUCT = 24 and SUM = -10
1     24	-1     -24
2     12	-2     -12
3     8	-3     -8
4     6	-4     -6

Step 7: Replace middle term $ -10 x $ with $ -4x-6x $:

$$ 8x^{2}-10x+3 = 8x^{2}-4x-6x+3 $$

Step 8: Apply factoring by grouping. Factor $ 4x $ out of the first two terms and $ -3 $ out of the last two terms.

$$ 8x^{2}-4x-6x+3 = 4x\left(2x-1\right) -3\left(2x-1\right) = \left(4x-3\right) \left(2x-1\right) $$

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