Question

Without actual dividion if 3 x minus 2 is a factor of 3 x cube + x square - 20 X + 12 then find other factors

Answer 1

Hello Mate!

So, without actual division we will use following steps.

Since 3x - 2 is factor so value of x = ⅔.

Let the given polynomial id ⅔

p(x) = 3x³ + x² - 20x + 12

p(⅔) = 3(⅔)³ + (⅔)² - 20(⅔) + 12

Since 3x - 2 is factor si according to factor theorum final value of p(x) should bd "0".

0 = 8/9 + 4/9 - 40/3 + 12

Taking L.C.M we get,

0 = ( 8 + 4 - 120 + 108 )/9

0 × 9 = 120 - 120

0 = 0

Hence proved that 3x - 2 is factor of p(x).

Now dividing p(x) by ( 3x - 2 ) we get, ( please see in attachment ).

So, p(x) = ( 3x - 2 )( x² + x - 6 )

p(x) = ( 3x - 2 )( x² + 3x - 2x - 6 )

p(x) = ( 3x - 2 )[ x( x + 3 ) - 2( x + 3 ) ]

p(x) = ( 3x - 2 )( x + 3 )( x - 2 )

So, x = - 3 and 2.

"Have great future ahead!"