2.5 – Apply the remainder and factor theorems

1. 2.5 – Apply the remainder and factor theorems Coach Bianco

2. Unit 2.5 – Apply the remainder and factor theorems • Georgia Performance Standards: • MM3A3c – Solve polynomial, exponential, and logarithmic inequalities analytically, graphically, and using appropriate technology. Represent solution sets of inequalities using interval notation.

3. Vocabulary • Polynomial long division – can be used to divide a polynomial f(x) by a divisor polynomial d(x), producing a quotient polynomial q(x) and a remainder polynomial r(x). • Synthetic division – can be used to divide any polynomial by a divisor of the form x – k. • Remainder Theorem – if a polynomial f(x) is divided by x – k, then the remainder is r = f(k). • Factor Theorem – a polynomial f(x) has a factor x – k, if and only if f(k) = 0.

4. Polynomial long division • Steps: • Set up like ANY long division problem you have done (Think 3rd grade!!) • Check for needed place holders (place holder = 0). • Multiply divisor to get first term • Always subtract – use parenthesis!! • Remainder goes over divisor at the end if you have one!

5. Polynomial long division • Divide f(x) = x2 + 3x + 6 by x + 1 using long division

6. Polynomial long division • Divide f(x) = x3 + 2 by x + 1 using long division

7. Try guided practice on page 86 (1 & 2)

8. Synthetic division • Steps: • Use the opposite (If it’s positive make it negative, if it’s negative make it positive) • Set up your “L” • Remember to check for placeholders (Standard form!!) • Drop it! • Multiply it! • Add it! • Remainder goes over the divisor if you have one!

9. Synthetic division • Divide f(x) = x3 + 2 by x + 1 using synthetic division

10. Synthetic division • Divide f(x) = x4 + 2x3 – 5x2 + 3x -1 by x - 1 using synthetic division.

11. Try guided practice on page 86 (#4)