find tge remainder using either remainder theorem or synthetic division
Answer (1)
The basic one is using the Synthetic Division. These are the final answers:-507Solutions:1.Write down the coefficient of the polynomial[tex] \frac{ {x}^{2} + 2 {x}^{2} + 7x + 1 }{ x + 1}[/tex]Coefficient - 1, 2, 7, 1[tex] - 1| \: \: 1 + 2 + 7 + 1[/tex]Bring down the first number, which is 1 and multiply it by -1. After that add after multiplying. Repeat. Bring down 1 1 * (-1) = 2 + (-1) = 11 * (-1) = 7 + (-1) = 66 * (-1) = 1 + (-6) = -5 (the remainder)2. Write down the coefficient of the polynomial[tex] \frac{ {x}^{5} + 4 {x}^{3} + 3}{x - 1} [/tex]Coefficient - 1, 0, - 4, 0, 0, 3Bring down the first number, which is 1 and multiply it by 1. After that add after multiplying. Repeat. Bring down 1 1 * 1 = 0 + 1 = 11 * 1 = (-4) + 1 = -3-3 * 1 = 0 + (-3) = -3-3 * 1 = 3 + (-3) = 0 (the remainder)3. Write down the coefficient of the polynomial[tex] \frac{11 {x}^{10} - \: 4 {x}^{7} }{x - 1} [/tex]Coefficient - 11, 0, 0, - 4, 0, 0, 0, 0, 0, 0Bring down the first number, which is 11 and multiply it by 1. After that add after multiplying. Repeat. Bring down 1111 * 1 = 0 + 11 = 1111 * 1 = 0 + 11 = 1111 * 1 = (-4) + 11 = 7 (the remainder)Example of using synthetic divisionhttps://brainly.ph/question/21964098What is synthetic division?https://brainly.ph/question/19403874https://brainly.ph/question/347390
