3x^3+5x^2-16x-2 factories
Answers
Answer:factorise : 3x^3 - 5x^2 - 16x + 12 = ( x - 3 ) ( 3x - 2 ) ( x + 2)
factorize P(x) = 3x^3 - 5x^2 - 16x + 12 = 0 is the correct question.
Here Consider grouping the first 2 terms and the remaining 2 terms for factorization.
x^2( 3x - 5 ) - 4 ( 4x - 3 ) = 0
This cannot be factorised directly.
Lets try to find a solution by trial and error.
X = 0 is clearly not a solution.
X = 1 , P ( 1 ) = 3 - 5 -16 + 12 = -6
x= 2 , p (2 ) = 3x8 - 5x 4 - 32 + 12 is not equal to 0.
X = 3 P( 3 ) = 3 .27 - 5 .9 - 48 + 12 = 81 - 45 - 48 -+ 12 = 0
Therfore x = 3 is a solution.
x - 3 is a factor.
Divide the P ( X ) by x -3 .
3x^3 - 5x^2 - 16x + 12 / x -3 = 3x^2 + 4x -4
factorising 3x^2 + 4x -4 = 3x^2 +6x - 2x -4 = 3x(x + 2) -2 ( x + 2)
==> ( 3x -2 ) ( x + 2 )
Therefore P (x) can be factorised as ( x -3 ) ( 3x - 2 ) ( x + 2 ) = 0
Therefore solutions are x = 3 , x = 2/3 , x = -2
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Answer:
3x^2+5x^2-16x-2
using identity
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