Problem 17 - College Algebra

Question

Divide using synthetic division. $$\left(2 x^{2}+x-10\right) \div(x-2)$$

Step-by-Step Solution

Answer

The quotient obtained after dividing \(2x^{2}+x-10\) with \(x-2\) is \(2x+5\)

Step 1: Set Up the Synthetic Division

Write down the coefficients of the polynomial \(2x^{2}+x-10\) in their order and the root of the divisor \(2\) in the lower left. It should look like this: \[ 2 \quad 1 \quad -10 \] \[ 2 \] where each number represents the coefficients of the polynomial in order from highest degree to lowest degree.

Step 2: Carry Out the Synthetic Division

Start by dropping down the leading coefficient then multiply it with the root and write it under the next coefficient then add those coefficients. Continue this process until all coefficients have been processed. We get the following: \[2 \quad 1+2*2=5 \quad -10+10=0\] \[2\] The numbers in the last row represent the coefficients of the quotient when the division is carried out.

Step 3: Interpret the Result

The numbers obtained in the last row of the synthetic division operation are the coefficients of the quotient: \(2x+5\)