factorise:

x³+13x²+32x+20  (by remainder theorem)

 

FIRST FIND OUT THE POSSIBLE ZEROES.

IN THIS POLYNOMIAL THE LAST  CONSTANT IS 20. THE ZEROES =1,-1, 2, -2, 4, -4, 5, -5, 10, -10

LET P(X)=X³+13X²+32X+20

LETS CHECK WITH -1

.'. P(-1) = (-1)³ + 13(-1)²+32(-1) +20

=  (-1) + 13 * 1 -32 +20

= (-1) +13 - 32 + 20

= 33 - 33

=0

SO, X = -1

. ' . ( X + 1) IS THE FACTOR OF P(X)

THEN DIVIDE X³+13X²+32X+20 WITH ( X + 1 )

YOU WILL GET  X² +12X + 20

EXPAND IT . YOU WILL GET X² + 10X +2X + 20

TAKE COMMON

= X( X+10) +2( X+10)

= (X + 10) ( X +2 )

. ' . THE FACTORS OF X³+13X²+32X+20 = ( X+1)( X+10)( X+2 )

THAT'S ALL

I HAVE EXPLAINED IT SO THAT YOU CAN UNDERSTAND. IT'S VERY SIMPLE

HOPE IT HELPED