Divide using synthetic division:

1. (2x^4 + 3x^3 + 2x - 3) : (x + 5)

2. (4x^3 + 5x^2 + 3x + 18) : (x + 2)

2x^3 - 7x^2 + 35x - 173 + 862 / (x+5) 4x^2 - 3x + 9

Step-by-step explanation:

The "divisor" is the root of the divisor expression, so is - 5 for the first problem and - 2 for the second one. The second row is added to the first row to get the third row. The third row is multiplied by the divisor (and shifted one place to the right) to make the second row.

Coefficients of the dividend are listed on the first row in descending order of degree from left to right, with 0 filling in for missing terms.

Numerous web pages and videos are available to describe the process in any level of detail you may desire.

The third row is the quotient coefficients, with the remainder appearing at the far right.