5 6 Find The Rational Zeros is another
- Slides: 8
5. 6 Find The Rational Zeros is another word for solutions.
List Possible Rational Zeros • Use p/q to find the possible rational zeros. • p represents the factors of the constant term • q represents the factors of the leading coeff. • (EX) x 3 + 2 x 2 – 11 x + 12 • p = factors of 12 (constant term) • q = factors of 1 (leading coefficient) • Make a list of all the possible combinations of p/q.
List the possible zeros of the polynomial below: • (EX) f(x) = 4 x 4 – x 3 – 3 x 2 + 9 x – 10 • (EX) f(x) = x 3 + 9 x 2 + 23 x + 15 • (EX) f(x) = 2 x 3 + 3 x 2 – 11 x – 6
Find zeros when the leading coefficient is 1. • Step 1: List the possible rational zeros. p/q • Step 2: Test the zeros using synthetic division. Use the possible factors as the substitution number until you get a remainder of 0. Step 3: Factor the trinomial and solve for x.
Find the zeros: • (EX) f(x) = x 3 – 8 x 2 + 11 x + 20 • (EX) f(x) = x 3 – 4 x 2 – 15 x + 18 • (EX) f(x) = x 3 – 8 x 2 + 5 x + 14
Find zeros when the leading coefficient is not 1. • (EX) f(x) = 10 x 4 – 11 x 3 – 42 x 2 + 7 x + 12 • Step 1: List the possible p/q • Step 2: Choose reasonable numbers by viewing the graph. • Step 3: Check the reasonable numbers using synthetic division • Step 4: Factor the polynomial. • Step 5: Repeat the steps above with the new polynomial
Practice Problem: • Find the zeros of the function: • (EX) 2 x 4 + 5 x 3 – 18 x 2 – 19 x + 42
CW/HW • Page 374 (3, 5, 7, 11, 13, 24)
