Factor polynomial $$ 4x^{2}-35x+24 $$

$$ 4x^{2}-35x+24 = ( x-8 )( 4x-3 ) $$

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:

$$ a = 4 , b = -35 ~ \text{ and } ~ c = 24 $$

Step 2: Multiply the leading coefficient $\color{blue}{ a = 4 }$ by the constant term $\color{blue}{c = 24} $.

$$ a \cdot c = 96 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = 96 $ and add to $ b = -35 $.

Step 4: All pairs of numbers with a product of $ 96 $ are:

PRODUCT = 96
1     96	-1     -96
2     48	-2     -48
3     32	-3     -32
4     24	-4     -24
6     16	-6     -16
8     12	-8     -12

Step 5: Find out which factor pair sums up to $\color{blue}{ b = -35 }$

PRODUCT = 96 and SUM = -35
1     96	-1     -96
2     48	-2     -48
3     32	-3     -32
4     24	-4     -24
6     16	-6     -16
8     12	-8     -12

Step 6: Replace middle term $ -35 x $ with $ -3x-32x $:

$$ 4x^{2}-35x+24 = 4x^{2}-3x-32x+24 $$

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

$$ 4x^{2}-3x-32x+24 = x\left(4x-3\right) -8\left(4x-3\right) = \left(x-8\right) \left(4x-3\right) $$

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