Mathematics 2004 JAMB Past Questions - Question 12: Find the remainder when 3x³ +5x² - 11x + 4 is divided by x + 3 .

Correct Answer

B

Explanation

To find the remainder when the polynomial 3x³ + 5x² - 11x + 4 is divided by x + 3, we can use the polynomial long division method.Let's set up the division:        3x² - 4x + 17    ___________________x + 3 | 3x³ + 5x² - 11x + 4To start, we divide the first term of the dividend (3x³) by the first term of the divisor (x), which gives us 3x². We then multiply the divisor (x + 3) by this quotient (3x²) and subtract it from the dividend:        3x² - 4x + 17    ___________________x + 3 | 3x³ + 5x² - 11x + 4        - (3x³ + 9x²)Simplifying, we get:        3x² - 4x + 17    ___________________x + 3 | 3x³ + 5x² - 11x + 4        - (3x³ + 9x²)        _______________                    -4x² - 11x + 4Next, we repeat the process with the new dividend (-4x² - 11x + 4) and the divisor (x + 3):        3x² - 4x + 17    ___________________x + 3 | 3x³ + 5x² - 11x + 4        - (3x³ + 9x²)        _______________                    -4x² - 11x + 4                    - (-4x² - 12x)                    _______________                                x + 4The remainder is x + 4.Therefore, the remainder when 3x³ + 5x² - 11x + 4 is divided by x + 3 is x + 4.