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If the sum of two consecutive odd integers is 20,
find the numbers

Factorise 2(x^3) - 3 (x^2)  - 3x +2

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algebra

If the sum of two consecutive odd integers is 20,
find the numbers

Let the numbers be x and y
If y is greater than x
y = x+2 -----------(1) [since consecutive odd integers
differ by 2 ]

given x + y = 20 -----------(2)

substitute (1) in (2)

x + (x+2) = 20

2x + 2 = 20

2x = 20 - 2

2x = 18

x = 18 / 2 = 9

y = x+2 = 9+2 = 11

The numbers are 9 and 11.
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problem2

Factorise 2(x^3) - 3 (x^2)  - 3x +2

let p(x) =
2(x^3) - 3 (x^2)  - 3x +2

p(-1)
  = -2 -3+3+2 = 0

therefore (x+1)  is a factor.

-1 [2 -3 -3 +2
**[0 -2+5 -2
----------------
**[2 -5 +2 (0

using sythetic division other factor is
2(x^2) -5x + 2 =
2(x^2) -4x -1x + 2
                  =2x[x-2]-1[x-2]

                        =[x-2][2x-1]

therefore p(x) = (x+1)
[x-2][2x-1]


other questions and problems:


*integral calculus integration formula





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