Dividing Polynomials: Long Division

Essential Question How do I use long division to divide polynomials?

WARMUP: (without a calculator) Divide 12,346 by 3… 3 ) 12346 4 1 1 5 How many times does 3 go into 12? 4.. so write that on top, multiply and subtract. – (12) Bring down the next number and repeat the process until you are out of numbers. 3 –(3)   4 –(3) 1 6 When you are out of numbers to bring down, any remainder is put as a fraction over the divisor! –(15) Now let’s divide some polynomials! 1

Simple Division - dividing a polynomial by a monomial It is as easy as dividing each term by the monomial!

Simplify

Simplify

Long Division - divide a polynomial by a polynomial Think back to long division from 3rd grade… How many times does the divisor go into the dividend? Put that number on top. Multiply that number by the divisor and put the result under the dividend. Subtract and bring down the next number in the dividend. Repeat until you have used all the numbers in the dividend. Any remainder is added as a fraction with the divisor as the denominator

x - 8 x2/x = x -8x/x = -8 -( ) + 3x x2 - 8x - 24 -( ) - 8x - 24

5. (h3 – 11h + 28)/(h – 4) h2 + 4h + 5 h3/h = h2 4h2/h = 4h 5h/h = 5 TIP: Use a zero as a coefficient for any missing terms/powers! + 4h + 5 h3/h = h2 4h2/h = 4h 5h/h = 5 -( ) - 4h2 h3 - 11h 4h2 -( ) 4h2 - 16h 5h + 28 -( ) 5h - 20 48

Assignment Complete the assigned worksheet.