Reminder steps for Long Division Dividing by Long Division. Steps 1.) Divide 1st term of dividend by first term of divisor. Put answer on top of dividing bar. This makes the quotient(answer) 2.) Multiply the answer in step 1 by the divisor and place them under the terms of the dividend with the same degree(exponent). 3.) Subtract. 4.) Repeat steps 1-3 until you can’t divide anymore. 5.) Once the degree of the dividend is lower then the divisor the remaining result is the remainder. If there is no remainder then the divisor was a factor.

Repeat 3x + 4 - ___-____ - ___-____ (3x2 – 11x – 26) ÷ (x – 5) 1st term of dividend is 3x2 3x + 4 1st term of divisor is x - ___-____ Repeat - ___-____

(3x3 + 11x2 + 4x + 1) ÷ (x2 + x)

Practice 1: (3x3 – x2 + x – 2) ÷ (x + 2)

Practice 2: (2x4 - 3x2 + x + 1) ÷ (2x2 + x + 1)

Dividing by Synthetic division Dividing by Synthetic Division. Only useful when the divisor is a degree 1 binomial. Steps 1.) Write all the Coefficients of the dividend in descending degree order. If a term is missing put a zero. 2.) Find the zero of the divisor (set = 0 and solve). This is the number you will synthetically divide by. 3.) Carry down the first coefficient. 4.) Multiply by the synthetic number put the answer under the next coefficient. 5.) Repeat until you have done this for the entire polynomial. 6.) If there is a remainder put it at the end over the divisor. If there is no remainder then the divisor was a factor.

5 2 3 25 x x – 5 = 0 ; x = 5 2 -7 10 + 10 15 (2x2 – 7x + 10) ÷ (x – 5) Step 1: bring the lead coefficient down. Step 2: multiply by the zero of the divisor. Step 3: place the answer to step 2 in the next column. Repeat steps 2 and 3 until the last column is done. Coefficients of the dividend in descending order 5 2 -7 10 + 10 15 2 3 25 x Start one degree down and use the numbers as your coefficients.

(x3 – 5x2 – 2) ÷ (x – 4) The dividends degrees must go down by one each time or you have to put a 0 in for the coefficient of that degree. x – 4 = 0 ; x = 4 Coefficients of the dividend in descending order since the x term is missing a 0 is put in its place 4 1 -5 0 -2 + 4 -4 -16 Step 1: bring the lead coefficient down. Step 2: multiply by the zero of the divisor. Step 3: place the answer to step 2 in the next column. Repeat steps 2 and 3 until the last column is done. 1 -1 -4 -18 x Start one degree down and use the numbers as your coefficients.

Practice 3: (x5 – 4x3 + x) ÷ (x + 3)

Practice 4: Use synthetic division to determine if x – c is a factor of the polynomial. 3x6 + 82x3 + 27; x + 3