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

Question

Mckayla Petersen

Mathematics

29 August, 20:14

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

+1

Answers (1)

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Rubi Barton · Answer 1

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