document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1106817>Question 1106817</A>: <I><SPAN STYLE=\"word-break: break-all;\"> when the polynomial p(x) is divided by (x-2) the remainder is 4 and when p(x) is divided by (x-3), the remainder is 7. And also if p(x) is a cubic function in which x³ is unity, q(x) is the quotient when divided by (x-2)(x-3)  and p(1)=1. determine q(x) and p(x).  </SPAN>\n" );
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document.write( "P(x)= (x-2)(x-3)Q(x)+ax+b, where Q(x) is the quotient;\r<BR>\n" );
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document.write( "Note that '(ax+b)' is the remainder after the division in every case.\r<BR>\n" );
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document.write( "P(2)= 2a+b = 4\r<BR>\n" );
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document.write( "P(3)= 3a+b = 7\r<BR>\n" );
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document.write( "a = 3, b = -2\r<BR>\n" );
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document.write( "Let Q(x) = x+c, where c is a constant and also due to the fact that the coefficient of x^3 is 1\r<BR>\n" );
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document.write( "P(x)=(x-2)(x-3)(x+c)+3x-2\r<BR>\n" );
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document.write( "P(1)= (1-2)(1-3)(1+c)+1=1\r<BR>\n" );
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document.write( "2(1+c)=0\r<BR>\n" );
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document.write( "c = -1\r<BR>\n" );
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document.write( "Q(x)= x-1\r<BR>\n" );
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document.write( "P(x) = (x-2)(x-3)(x-1)+3x-2\r<BR>\n" );
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document.write( "P(x)= x^3-6x^2+14x-8<BR>\n" );
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