Solution - Simplification or other simple results

5 x \cdot (2 x^{2} - 2 x - 3)

5x*(2x^2-2x-3)

Step by Step Solution

Step 1 :

Equation at the end of step 1 :

  ((10 • (x³)) -  (2•5x²)) -  15x
 Step  2  :

Equation at the end of step 2 :

  ((2•5x³) -  (2•5x²)) -  15x

Step 3 :

Step 4 :

Pulling out like terms :

4.1 Pull out like factors :

10x³ - 10x² - 15x = 5x • (2x² - 2x - 3)

Trying to factor by splitting the middle term

4.2 Factoring 2x² - 2x - 3

The first term is, 2x² its coefficient is 2 .
The middle term is, -2x its coefficient is -2 .
The last term, "the constant", is -3

Step-1 : Multiply the coefficient of the first term by the constant 2 • -3 = -6

Step-2 : Find two factors of -6 whose sum equals the coefficient of the middle term, which is -2 .

-6	+	1	=	-5
-3	+	2	=	-1
-2	+	3	=	1
-1	+	6	=	5

Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored

Final result :

  5x • (2x² - 2x - 3)

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