Factories using theorem p(x) = x^3 + 13x^2 + 32x + 20
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Anil Singh Kunwar asked in Math
factorise:
x3+13x2+32x+20 (by remainder theorem)
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Nitheesh Pillai answered this
71 helpful votes in Math, Class IX
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
Anonymous619:
Synthetic method is exactly what I was looking for
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