Activity 2: Divide the following polynomials using long division. Showcomplete solution in your answer sheet.a) (2x3+9x²+3x-4)+(x+4)b) (8x3+27) (2x+3)
Answer (1)
a) Divide (2x^3 + 9x^2 + 3x - 4) by (x + 4):Setup: Divide 2x^3 + 9x^2 + 3x - 4 by x + 4.First Division: Divide 2x^3 by x to get 2x^2. Write 2x^2 above the division line.Multiply: Multiply 2x^2 by (x + 4) to get 2x^3 + 8x^2.Subtract: Subtract 2x^3 + 8x^2 from 2x^3 + 9x^2 + 3x - 4 to get x^2 + 3x - 4.Next Division: Divide x^2 by x to get x. Write x above the division line.Multiply: Multiply x by (x + 4) to get x^2 + 4x.Subtract: Subtract x^2 + 4x from x^2 + 3x - 4 to get -x - 4.Final Division: Divide -x by x to get -1. Write -1 above the division line.Multiply: Multiply -1 by (x + 4) to get -x - 4.Subtract: Subtract -x - 4 from -x - 4 to get 0.The quotient is 2x^2 + x - 1 with no remainder.b) Divide (8x^3 + 27) by (2x + 3):Setup: Divide 8x^3 + 27 by 2x + 3.First Division: Divide 8x^3 by 2x to get 4x^2. Write 4x^2 above the division line.Multiply: Multiply 4x^2 by (2x + 3) to get 8x^3 + 12x^2.Subtract: Subtract 8x^3 + 12x^2 from 8x^3 + 27 to get -12x^2 + 27.Next Division: Divide -12x^2 by 2x to get -6x. Write -6x above the division line.Multiply: Multiply -6x by (2x + 3) to get -12x^2 - 18x.Subtract: Subtract -12x^2 - 18x from -12x^2 + 27 to get 18x + 27.Final Division: Divide 18x by 2x to get 9. Write 9 above the division line.Multiply: Multiply 9 by (2x + 3) to get 18x + 27.Subtract: Subtract 18x + 27 from 18x + 27 to get 0.The quotient is 4x^2 - 6x + 9 with no remainder.
