Factor polynomial $$ -2x^{2}+19x-35 $$

$$ -2x^{2}+19x-35 = -( x-7 )( 2x-5 ) $$

Step 1 :

After factoring out $ -1 $ we have:

$$ -2x^{2}+19x-35 = - ~ ( 2x^{2}-19x+35 ) $$

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:

$$ a = 2 , b = -19 ~ \text{ and } ~ c = 35 $$

Step 3: Multiply the leading coefficient $\color{blue}{ a = 2 }$ by the constant term $\color{blue}{c = 35} $.

$$ a \cdot c = 70 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = 70 $ and add to $ b = -19 $.

Step 5: All pairs of numbers with a product of $ 70 $ are:

PRODUCT = 70
1     70	-1     -70
2     35	-2     -35
5     14	-5     -14
7     10	-7     -10

Step 6: Find out which factor pair sums up to $\color{blue}{ b = -19 }$

PRODUCT = 70 and SUM = -19
1     70	-1     -70
2     35	-2     -35
5     14	-5     -14
7     10	-7     -10

Step 7: Replace middle term $ -19 x $ with $ -5x-14x $:

$$ 2x^{2}-19x+35 = 2x^{2}-5x-14x+35 $$

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

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

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