Factorise 3x cube +5x square-16x-2
Answers
Factorise :
3x³- 5x² - 16x + 12 = ( x - 3 ) ( 3x - 2 ) ( x + 2)
Factorize:—
P(x) = 3x³ - 5x² - 16x + 12 = 0 is the correct question.
Here,
Consider grouping the first 2 terms and the remaining 2 terms for factorization.
x²( 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
Therefore,
x = 3 is a solution.
x - 3 is a factor.
Divide the P ( X ) by x -3 .
3x³- 5x² - 16x + 12 / x -3 = 3x² + 4x - 4
Factorising,
3x² + 4x - 4 = 3x² + 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
