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 ) = 4 x 5 + 37 x 4 + 117 x 3 + 87 x 2 − 193 x − 52 ; − 3 + 2 i and − 1 4 are zeros
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 ) = 4 x 5 + 37 x 4 + 117 x 3 + 87 x 2 − 193 x − 52 ; − 3 + 2 i and − 1 4 are zeros
Solution Summary: The author calculates the zeroes of the polynomial f(x)=4x
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
In Exercises 130–133, use a graphing utility to graph the
functions y, and y2. Select a viewing rectangle that is
large enough to show the end behavior of y2. What can
you conclude? Verify your conclusions using polynomial
multiplication.
130. yı = (x - 2)²
y2 = x2 – 4x + 4
131. yı = (x – 4)(x²
y2 = x - 7x2 + 14x – 8
132. yı = (x – 1)(x + x + 1)
y2 = x – 1
133. yı = (x + 1.5)(x – 1.5)
y2 = x? – 2.25
3x + 2)
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