Long Division What is a Polynomial Remember a

Long Division

What is a Polynomial? Remember, a polynomial is just a number of terms separated by + and – signs. A term isn’t allowed to be anything too funky, so a polynomial doesn’t have any really weird parts. This is an ordinary polynomial:

What is a Binomial? “Binomial” is just another name for a polynomial with 2 terms.

A Division Problem What if they ask us to divide a polynomial by a binomial? We would have to use long division:

Long Division Remember long division from grade school?

It’s not that hard! Just break it into parts. Take the outside number into the beginning of the inside number.

Same here Take the outside number into the beginning of the inside number.

It’s not that hard! What number times 12 gives a number close to (but not bigger than) 62?

Same here What times x would give you

Now multiply Multiply the top times the outside number:

Same here Multiply the top times the whole outside: Common mistake: Forgetting to multiply the 2

Now subtract Change the sign on the bottom and combine

Same here Change the signs on the bottom and combine:

Bring it on! Bring down the next number

Same here Bring down the rest of the number

Rinse and repeat Here we go again – first into first

Same here Here we go again – first into first

Rinse and repeat Here we go again – multiply

Same here Here we go again – first into first

Rinse and repeat Here we go again – change the signs on the bottom and combine

Same here Here we go again – change the signs on the bottom and combine

Things that can be weird Remainders: If you don’t get zero as a remainder, make a fraction with the remainder as the top and the outside polynomial as the bottom.

Things that can be weird Remainders: If you don’t get zero as a remainder, make a fraction with the remainder as the top and the outside polynomial as the bottom.

Things that can be weird Missing pieces: If your polynomial is missing pieces, fill in with zeros as place-holders.

Things that can be weird Out of order: Make sure your polynomial is written with the exponents in order from biggest to smallest.

Long Division Be sure polynomials are in descending order of exponents Take the first part into the first part. Multiply Change the signs on the bottom and combine. Bring down the rest of the “inside”. Rinse and repeat.