Ch 8'5 Rational Root Theorem

1
Ch 8.5 Rational Root Theorem

• If is a fraction in simplest form and is a
  zero of the polynomial f(x), then
• P factor of the final term (term with no
  variable)
• Q factor of the first term (highest degree term)

Ex Find the possible rational roots of
P ( factors of -10)
Q (factors of 3)
2
Find all the rational zeros

• Find all the possible zeros
• Use Descartes rule of signs (8.4) to determine
  the number of positive and negative roots
• Use synthetic division or the remainder theorem
  to figure out the roots (roots of the polynomial
  will make the remainder be zero)

3
Find the rational zeros for
Possible roots ,so
Descartes
Positive
no
yes
no
Negative
yes
no
yes
Positive 1 Negative 2 or 0
Continued
4
Remainder Theorem
Positive
NO
YES!
Negative
YES!
NO
YES!
Roots (Solutions of polynomial) 2, -1, -4