Long Division of Polynomial
• To divide 2x^4 + x^3 + 4x^2 - 3x - 2 by x - 3, we will use long division method.
• First, we set up the division like regular long division, with the dividend (2x^4 + x^3 + 4x^2 - 3x - 2) inside the bracket and the divisor (x - 3) outside the bracket.
• We start by dividing the first term of the dividend by the divisor, which gives us 2x^3.
• We multiply the divisor (x - 3) by the quotient we just found (2x^3), which gives us 2x^4 - 6x^3.
• Next, we subtract this product from the original dividend, which gives us -5x^3 + 4x^2 - 3x - 2.
• We repeat the process with the new dividend (-5x^3 + 4x^2 - 3x - 2) by dividing the first term by the divisor, which gives us -5x^2.
• We continue this process until we have no more terms to bring down.
• The final result of the division is the quotient 2x^3 - 5x^2 + 16x - 46 with a remainder of 136.
• Therefore, 2x^4 + x^3 + 4x^2 - 3x - 2 divided by x - 3 is equal to 2x^3 - 5x^2 + 16x - 46 with a remainder of 136.