mac1105_lecture19_1

mac1105_lecture19_1 - L19 Zeros of a Polynomial Function...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
200 L19 Zeros of a Polynomial Function Division Algorithm for Polynomials If f and g are two polynomials and g is not the zero polynomial, then there are the unique polynomials q (quotient) and r (remainder) such that () fx rx qx gx =+ o r ()() () fx qxgx rx = + where ( ) either the zero polynomial or of degree less than the degree of ( ) . Note : If ( ) x c =− , then ( ) ( )( ) fx qxx c r = −+ , where r is a number. If x c = , then ( ) fc = Remainder Theorem If a polynomial ( ) is divided by ( ) x c , then the remainder ( ) rf c = .
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
201 Example : Find the remainder if 43 () 6 2 fx x x = −+ is divided by ( 2) x + . Use synthetic division the Remainder Theorem Example : Use the Remainder Theorem to find (3) f if 65 2 6 5 4 1 6 1 x x x =− + +
Background image of page 2
202 Note : If the polynomial ( ) fx is divided by ( ) x c and the remainder 0 r = , then ( ) 0 fc = , that is, c is a zero of ( ) . Example : If 3 () 6 4 fx x x =−+ , is 2 a zero of f ? Factor Theorem The polynomial ( ) x c is a factor of the polynomial if and only if ( ) 0 = . Proof : If ( ) x c is a factor of f , then ( ) = hence ( ) = If ( ) 0 = , then ( ) r f c = = and ( ) = therefore ( ) x c is a factor of f .
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
203 Example : Is ( 1) x
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 11

mac1105_lecture19_1 - L19 Zeros of a Polynomial Function...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online