If p/q is a rational number in lowest terms and if it is a zero of
f(x) = 10x4
+ ax3 + bx2 + 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) = 8x3 + 2x2 + 4x +1
Give all the possible rational zeros of f
using the rational zero theorem:
f(x) = x4 + 3x2
f(x) = 8x4 – 2x3
+ x + 15
Use the Rational–Zero Theorem to find rational zeros of g if g(x) = x3 – 9x.
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) = x3 – 3x2
+ 9x – 27, x = 3i
Use synthetic division to decide which of the factors 1, –1, 3 and –3 are zeros of the function:
f(x) = x3 + 5x2 – 9x – 45
f(x) = x4 + 4x3 + 4x2 – 4x
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.
– 12x + 36 = 0
Find all the roots of the following equation by factoring and solving the resulting quadratic equations.
z4 – 16 = 0
Determine all the real zeros of the function:
f(x) = x3 – 9x2 – 40x + 48
f(x) = x3 – 9x2 + 8x + 60
Determine all the zeros of the polynomial function.
f(x) = x4 + 4x3
– x2 – 16x – 12
f(x) = x3 – x2
+ 81x – 81
f(x) = x4 + 8x3
+ 16x2 + 32x + 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
2i, –2i, 3
5, 5, 3 + i
One of the zeroes of the function f(x) = x3 – 7x2
+ 13x – 6 is at x = 2. Determine the other zeroes.
One of the zeroes of the function f(x) = 3x3 + 5x2
+ 4 is at x = –2. Determine the other zeroes.
Given one zero of the polynomial function, determine the other zeros.
f(x) = x3 + 2x2
+ x + 36, –4
Choose any method to find all the real zeroes of f(x) = x4 – 5x2 – 7.