If polynomial x³ + 11x² +31x + 21 has (x + 3) as a factor then, find the remaining factors.
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Answer:
The remaining factors are: (x+1)(x+7)
Step-by-step explanation:
x3+11x2+31x+21
=x3+3x2+8x2+24x+7x+21(as above mentioned x+3 is a factor so first approach to that)
=x2(x+3)+8x(x+3)+7(x+3)
=(x2+8x+7)(x+3)
=(x2+7x+x+7)(x+3)
=(x(x+7)+1(x+7))(x+3)
=(x+3)(x+1)(x+7)
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