{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# 3_4 - Section 3.4 The Real Zeros of a Polynomial Function...

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

Section 3.4: The Real Zeros of a Polynomial Function Instructor: Ms. Hoa Nguyen 1 The Remainder If f ( x ) and g ( x ) are polynomials, then f ( x ) g ( x ) = q ( x ) + r ( x ) g ( x ) (1) f ( x ): the dividend g ( x ): the divisor ( g ( x ) = 0) q ( x ): the quotient r ( x ): the remainder Remark : r ( x ) has a degree less than the degree of g ( x ). Example 1 Example 2 1

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

View Full Document
Example 3 : Find the quotient and the remainder of f ( x ) g ( x ) with f ( x ) = x 3 + 2 x 2 + x - 1 and g ( x ) = x - 2. Compute f (2) then compare with the remainder . The Remainder Theorem: If g ( x ) = x - c then the remainder of f ( x ) g ( x ) is f ( c ). 2
2 The Factor Theorem r is a zero of the polynomial f ( x ) ⇐⇒ f ( r ) = 0 ⇐⇒ the term ( x - r ) is a factor of f . Example 4 Theorem : Every polynomial of real coefficients a n , a n - 1 , · · · , a 1 , a 0 can be factored into factors that are either LINEAR factors or IRREDUCIBLE QUADRATIC factors. An irreducible quadratic factor is a quadratic function whose discriminant ( b 2 - 4 ac ) is NEGATIVE . Remark : A polynomial of degree n cannot have more than n zeros. Example 5 Example 6 Example 7 3

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

View Full Document
3 The Rational Zeros Theorem Given a polynomial f with integer coefficients a n , a n - 1 , · · · , a
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 5

3_4 - Section 3.4 The Real Zeros of a Polynomial Function...

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

View Full Document
Ask a homework question - tutors are online