Factor polynomial $$ 8x^{2}+60x+112 $$

$$ 8x^{2}+60x+112 = 4( 2x+7 )( x+4 ) $$

Step 1 :

After factoring out $ 4 $ we have:

$$ 8x^{2}+60x+112 = 4 ( 2x^{2}+15x+28 ) $$

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:

$$ a = 2 , b = 15 ~ \text{ and } ~ c = 28 $$

Step 3: Multiply the leading coefficient $\color{blue}{ a = 2 }$ by the constant term $\color{blue}{c = 28} $.

$$ a \cdot c = 56 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = 56 $ and add to $ b = 15 $.

Step 5: 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 6: Find out which factor pair sums up to $\color{blue}{ b = 15 }$

PRODUCT = 56 and SUM = 15
1     56	-1     -56
2     28	-2     -28
4     14	-4     -14
7     8	-7     -8

Step 7: Replace middle term $ 15 x $ with $ 8x+7x $:

$$ 2x^{2}+15x+28 = 2x^{2}+8x+7x+28 $$

Step 8: Apply factoring by grouping. Factor $ 2x $ out of the first two terms and $ 7 $ out of the last two terms.

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

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