Divide and check whether the g(x) is factor of p(x) by division algorithm. (a) p(x)=x4-3x3+4*2-8x+4; g(x)=x2-x+2 (b) p(x)=2x4-3*3-3x +6x-2, g(x)=x2-2
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Here, the dividend is x
2
+4x+4, the divisor is x+2, the quotient is x+2 and the remainder is 0, therefore,
x
2
+4x+4=[(x+2)(x+2)]+0
⇒x
2
+4x+4=[x(x+2)+2(x+2)]
⇒x
2
+4x+4=x
2
+2x+2x+4
⇒x
2
+4x+4=x
2
+4x+4
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