Problem 18 - College Algebra

Question

Divide using synthetic division. $$\left(x^{2}+x-2\right) \div(x-1)$$

Step-by-Step Solution

Answer

The quotient of the polynomial division is \(x+2\).

Step 1: Identify the Coefficients and Setup Synthetic Division

Write out the coefficients of the polynomial \(x^{2}+x-2\) we are dividing, which are [1, 1, -2]. Write out the value of 'x' from the divisor, \(x-1\), which gives us 1. Set up the synthetic division where the coefficients of the polynomial are on the top row and the 'x' value is on the left outside the division symbol.

Step 2: Perform the Synthetic Division

Start synthetic division by bringing down the leading coefficient (1) in the dividend to the bottom row. Multiply this number by the divisor (1), and write the result (1) under the next coefficient in the top row. Add the numbers in this column together and write the sum underneath (1+1=2). Repeat this process with this new number (2). Multiply it with the divisor (2*1=2), write the result under the next coefficient, and add the column to get 0.

Step 3: Write the Result

The final row of numbers represents the coefficients of the quotient. In our case, [1, 2, 0] represents the function \(x+2\). Thus, \((x^{2}+x-2) \div (x-1)\) results in \(x+2\).