Factor polynomial $$ 7x^{2}-30x+8 $$

$$ 7x^{2}-30x+8 = ( x-4 )( 7x-2 ) $$

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:

$$ a = 7 , b = -30 ~ \text{ and } ~ c = 8 $$

Step 2: Multiply the leading coefficient $\color{blue}{ a = 7 }$ by the constant term $\color{blue}{c = 8} $.

$$ a \cdot c = 56 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = 56 $ and add to $ b = -30 $.

Step 4: All pairs of numbers with a product of $ 56 $ are:

PRODUCT = 56
1     56	-1     -56
2     28	-2     -28
4     14	-4     -14
7     8	-7     -8

Step 5: Find out which factor pair sums up to $\color{blue}{ b = -30 }$

PRODUCT = 56 and SUM = -30
1     56	-1     -56
2     28	-2     -28
4     14	-4     -14
7     8	-7     -8

Step 6: Replace middle term $ -30 x $ with $ -2x-28x $:

$$ 7x^{2}-30x+8 = 7x^{2}-2x-28x+8 $$

Step 7: Apply factoring by grouping. Factor $ x $ out of the first two terms and $ -4 $ out of the last two terms.

$$ 7x^{2}-2x-28x+8 = x\left(7x-2\right) -4\left(7x-2\right) = \left(x-4\right) \left(7x-2\right) $$

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