If * ^{p}*/

*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

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

*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*.

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

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

*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

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

3, 1, 5

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

–1, –3, –8

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

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.