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
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)
Determine which functions have two real number zeros by calculating the discriminant, b2 – 4ac. Check all that
apply.
O fx) = x² + 6x + 8
O g(x) = x² + 4x + 8
O h(x) = x2 – 12x + 32
O k(x) = x2 + 4x – 1
O p(x) = 5x2 + 5x + 4
O t(x) = x2 – 2x – 15
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2) Show that a3 + b³ = (a + b)(a² – ab + b²) is a polynomial identity.
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