# Hotmath

If
*
^{
p
}
*
/

*is a rational number in lowest terms and if it is a zero of*

_{ q }
*
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
*
.

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

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

Determine all the zeros of the polynomial function.

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

Determine all the zeros of the polynomial function.

*
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

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.