Question

factorise 2x ki power 3 minus 9 X square + X + 12​

Answer 1

Answer:

Solution:  Use hit and trial method..  take a factor x = -1  ⇒ f(x)=-1

Substituting the equation we get..

⇒ f(1)= 2(-1)³ - 9(-1)² + (-1) + 12

⇒ -2+9-1+12

⇒ 9 - 9

⇒0

∴ (x+1) is a factor of 2x³ - 9x² + x +12  Now we divide 2x³ - 9x² + x +12 by (x+1)           2x³ - 11x + 12

x+1) 2x³ - 9x² + x +12       - 2x³ - 2x²               -11x² +x               +11x² +11x                          12x + 12                         -12x - 12                                 ×      

By dividing we get quadratic: 2x³ - 11x + 12  We find roots by solving for x;  x = [-b +(or) - √( b² - 4ac)]/ 2a

x = [ 11 +(or) - √ (121- 96)]/4

x = [ 11 +(or) - √25]/4

we get x =4 or x = 3/2;  therefor (x+1),(x-4) and (2x-3) are all factors of 2x³ - 9x² + x + 12.