Factor polynomial $$ 4x^{2}+38x+70 $$

$$ 4x^{2}+38x+70 = 2( 2x+5 )( x+7 ) $$

Step 1 :

After factoring out $ 2 $ we have:

$$ 4x^{2}+38x+70 = 2 ( 2x^{2}+19x+35 ) $$

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 $ 14x+5x $:

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

Step 8: Apply factoring by grouping. Factor $ 2x $ out of the first two terms and $ 5 $ out of the last two terms.

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

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