Question

Divide. Divide \(a^{2}-3 a+2\) by \(a-1\)

Short answer

The division of \(a^{2}-3 a+2\) by \(a-1\) gives \(a-2\) as quotient with remainder \(0\).

Step-by-step solution

Set up synthetic division

First, set up synthetic division. Write the coefficients of the numerator polynomial \(a^{2}-3 a+2\) along the top row, which would be \(1, -3, 2\). Next, determine what number to use in the synthetic division process. If we are dividing by the term \(a - 1\), that number would be \(1\).

Perform synthetic division

In synthetic division: \n 1. Bring down the leading coefficient (which in this case is \(1\)). This forms the leading coefficient of the resulting polynomial. \n 2. Multiply the number just written on the bottom row by the constant in the box (also \(1\) here), then write this value under the next coefficient on the top. \n 3. Add the numbers in this second column together and write the result on the bottom. \n 4. Continue steps 2-3 until all coefficients on the top have been used. \n So, for our case we have first \(1\) then, multiply this with \(1\) gives \(1\), after adding to \(-3\) we get \(-2\), multiply this with \(1\) gives \(-2\), then adding to \(2\) finally gets \(0\). \n Hence bottom row becomes \(1, -2, 0\).

Write the solution in polynomial terms

Now we write this bottom row values as coefficients in the polynomial (revealing the result of the division). Starting with power \(n-1\) where \(n\) is degree of upper polynomial and goes down, we get \(a-2\) as quotient and remainder is \(0\).