For Exercises 33–38, a polynomial f ( x ) and one or more of its zeros is given . a. Find all the zeros. b. Factor f ( x ) as a product of linear factors. c. Solve the equation ( x ) = 0 f. (See Example 5) f ( x ) = 3 x 3 − 28 x 2 + 83 x − 68 ; 4 + i is a zero
For Exercises 33–38, a polynomial f ( x ) and one or more of its zeros is given . a. Find all the zeros. b. Factor f ( x ) as a product of linear factors. c. Solve the equation ( x ) = 0 f. (See Example 5) f ( x ) = 3 x 3 − 28 x 2 + 83 x − 68 ; 4 + i is a zero
Solution Summary: The author calculates the zeroes of the polynomial f(x)=3x
For Exercises 23–24, use the remainder theorem to determine
if the given number c is a zero of the polynomial.
23. f(x) = 3x + 13x + 2x + 52x – 40
a. c = 2
b. c =
24. f(x) = x* + 6x + 9x? + 24x + 20
а. с 3D —5
b. c = 2i
For Exercises 115–120, factor the expressions over the set of complex numbers. For assistance, consider these examples.
• In Section R.3 we saw that some expressions factor over the set of integers. For example: x - 4 = (x + 2)(x – 2).
• Some expressions factor over the set of irrational numbers. For example: - 5 = (x + V5)(x – V5).
To factor an expression such as x + 4, we need to factor over the set of complex numbers. For example, verify that
x + 4 = (x + 2i)(x – 2i).
115. а. х
- 9
116. а. х?
- 100
117. а. х
- 64
b. x + 9
b. + 100
b. x + 64
118. а. х — 25
119. а. х— 3
120. а. х — 11
b. x + 25
b. x + 3
b. x + 11
For questions 10 – 11, use the table to answer the questions. It is set up to multiply
two polynomials. (show your work)
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