1. Divide the following polynomials by synthetic division method. Write the quotient and the
remainder
((x + 2x + 3x + 4x +5 ) + (x+2)
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Answer:
linear division method
(x
4
+2x
3
+3x
2
+4x+5)÷(x+2)
=x
3
(x+2)−2x
3
+2x
3
+3x
2
+4x+5
=x
3
(x+2)+3x
2
+4x+5
=x
3
(x+2)+3x(x+2)−6x+4x+5
=x
3
(x+2)+3x(x+2)−2x+5
=x
3
(x+2)+3x(x+2)−2(x+2)+4+5
=x
3
(x+2)+3x(x+2)−2(x+2)+9
=(x+2)(x
3
+3x−2)+9
quotient =x
3
+3x−2
remainder =9
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