Algebra 2
Notes – Lesson 6.3
Name _________________________________
Synthetic Division.
Divide 3x3 – 4x2 + 2x – 1 by x + 1 (show your work off to the right of the steps listed)
Step 1:
Change the sign of the constant term in the divisor.
Write the coefficients of the polynomial in standard form.
Step 2:
Bring down the first coefficient.
Step 3:
Multiply the first coefficient by the new divisor.
Write the result under the next coefficient. Add.
Step 4:
Repeat the steps of multiplying and adding until the remainder is found.
Examples.
(x3 – 4x2 + 6x – 4)  (x – 2)
(-2x3 + 5x2 – x + 2)  (x + 2)
(x4 – 5x2 + 4x + 12)  (x + 2)
Is x + 3 a factor of 3x2 + 10x2 – x – 12
Use synthetic division and the give factor to completely factor each polynomial function.
y = x3 + 3x2 – 13x – 15; (x + 5)
y = x3 – 3x2 – 10x + 24; (x – 2)