Factor polynomial $$ 2x^{2}+17x+35 $$

$$ 2x^{2}+17x+35 = ( 2x+7 )( x+5 ) $$

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:

$$ a = 2 , b = 17 ~ \text{ and } ~ c = 35 $$

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

$$ a \cdot c = 70 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = 70 $ and add to $ b = 17 $.

Step 4: 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 5: Find out which factor pair sums up to $\color{blue}{ b = 17 }$

PRODUCT = 70 and SUM = 17
1     70	-1     -70
2     35	-2     -35
5     14	-5     -14
7     10	-7     -10

Step 6: Replace middle term $ 17 x $ with $ 10x+7x $:

$$ 2x^{2}+17x+35 = 2x^{2}+10x+7x+35 $$

Step 7: Apply factoring by grouping. Factor $ 2x $ out of the first two terms and $ 7 $ out of the last two terms.

$$ 2x^{2}+10x+7x+35 = 2x\left(x+5\right) + 7\left(x+5\right) = \left(2x+7\right) \left(x+5\right) $$

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