2.2 D IVIDING POLYNOMIALS ; R EMAINDER AND F ACTOR T HEOREMS.

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Presentation transcript:

2.2 D IVIDING POLYNOMIALS ; R EMAINDER AND F ACTOR T HEOREMS

R EVIEW O F F ACTORS What is a factor? How do you know if 4 is a factor of 50? Is 4 a factor of 124?

LONG DIVISION REVIEW r1

L ONG D IVISION OF P OLYNOMIALS

E XAMPLE Divide using long division. State the quotient, q( x ), and the remainder, r( x ). (6x ³ +17x²+ 27x + 20) (3x + 4)

E XAMPLE Divide using long division. State the quotient, q( x ), and the remainder, r( x ).

R EMAINDERS CAN BE USEFUL ! THE REMAINDER THEOREM : If the polynomial P(x) is divided by (x – a), then the remainder is P(a).

S YNTHETIC D IVISION Quick method of dividing polynomials Used when the divisor is of the form x – a Last column is always the remainder

E XAMPLE Divide using synthetic division.

E XAMPLE Divide using synthetic division.

F ACTOR T HEOREM For a polynomial P(x), x-a is a factor if an only if P(a)=0 Or in other words, If f(c) = 0, then x – c is a factor of f(x). If x – c is a factor of f(x), then f(c) = 0. If we know a factor, we know a zero! If we know a zero, we know a factor!

PG. 61 # 20 You are given the polynomial and one of the roots are x= -2. Find the other roots.

PG. 61 # 22 You are given the polynomial two of the roots are x= -2 and x=3. Find the other roots.