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what is the remainder when 2x^3+3x^2+x+1 is divided by x+3

Sagot :

2x^3 + 3x^2 + x + 1
=2x^3 + 3x^2 + 3x^2 - 3x^2 + x + 1
=2x^3 + 6x^2 - 3x^2 + x + 1
=2(x^3 + 3x^2) - 3x^2 + x + 1
=2x^2*(x+3) - 3x^2 -9x + 9x + x +1
=2x^2*(x+3) - 3x(x+3) + 10x +1
=2x^2*(x+3) - 3x(x+3) + 10x + 30 - 30 +1
=2x^2*(x+3) - 3x(x+3) +10(x+3) -29

The first three terms can be divided by (x+3) evenly so the remainder is -29
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