2.5 – Apply the remainder and factor theorems Coach Bianco

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.

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.

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!

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

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

Try guided practice on page 86 (1 & 2)

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!

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

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

Try guided practice on page 86 (#4)