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If ^{ p } / _{ q } is a rational number in lowest terms and if it is a zero of

f ( x ) = 10 x ^{ 4 } + ax ^{ 3 } + bx ^{ 2 } + cx + 3, what is true about p and q ? List the possible rational zeros of f .

Obtain the possible rational zeros of the given polynomial, using the Rational –Zero Theorem.

P ( x ) = 8 x ^{ 3 } + 2 x ^{ 2 } + 4 x +1

Give all the possible rational zeros of f using the rational zero theorem:

f ( x ) = x ^{ 4 } + 3 x ^{ 2 } – 36

f ( x ) = 8 x ^{ 4 } – 2 x ^{ 3 } + x + 15

Use the Rational–Zero Theorem to find rational zeros of g if g ( x ) = x ^{ 3 } – 9 x .

Use an alternate technique to find the rational zeros of g .

Tell whether the given x –value is a zero of the function.

f ( x ) = x ^{ 3 } – 3 x ^{ 2 } + 9 x – 27, x = 3 i

Use synthetic division to decide which of the factors 1, –1, 3 and –3 are zeros of the function:

f ( x ) = x ^{ 3 } + 5 x ^{ 2 } – 9 x – 45

f ( x ) = x ^{ 4 } + 4 x ^{ 3 } + 4 x ^{ 2 } – 4 x – 5

Choose a statement that is true about the given quantities:

A. The quantity in column A is greater.

B. The quantity in column B is greater.

C. The two quantities are equal.

D. The relationship cannot be determined from the given information.

Solve the given equation. Identify whether the given equation has any multiple roots.

x ^{ 2 } – 12 x + 36 = 0

Find all the roots of the following equation by factoring and solving the resulting quadratic equations.

z ^{ 4 } – 16 = 0

Determine all the real zeros of the function:

f ( x ) = x ^{ 3 } – 9 x ^{ 2 } – 40 x + 48

f ( x ) = x ^{ 3 } – 9 x ^{ 2 } + 8 x + 60

Determine all the zeros of the polynomial function.

f ( x ) = x ^{ 4 } + 4 x ^{ 3 } – x ^{ 2 } – 16 x – 12

f ( x ) = x ^{ 3 } – x ^{ 2 } + 81 x – 81

f ( x ) = x ^{ 4 } + 8 x ^{ 3 } + 16 x ^{ 2 } + 32 x + 48

Write a polynomial function of least degree that has real coefficients, the given zeros, and a leading coefficient of 1.

3, 1, 5

–1, –3, –8

2 i , –2 i , 3

5, 5, 3 + i

One of the zeroes of the function f ( x ) = x ^{ 3 } – 7 x ^{ 2 } + 13 x – 6 is at x = 2. Determine the other zeroes.

One of the zeroes of the function f ( x ) = 3 x ^{ 3 } + 5 x ^{ 2 } + 4 is at x = –2. Determine the other zeroes.

Given one zero of the polynomial function, determine the other zeros.

f ( x ) = x ^{ 3 } + 2 x ^{ 2 } + x + 36, –4

Choose any method to find all the real zeroes of f ( x ) = x ^{ 4 } – 5 x ^{ 2 } – 7.