Name: ________________________________________
DUE WED DEC 3
Solve each equation!
1.
250x4 = 2x
2.
2x3 – 8x2 + 10x = 40
3.
–3x4 + 243 = 0
4.
–3x5 + 15x3 + 108x = 0
5.
–27x5 + 48x = 0
6.
4x3 + 8x2 = 9 (x + 2)
7.
36m6 + 12m4 + m2 = 0
8.
28x4 – 79x = 4x4 + 2x
9.
Solve.
10.
x4 + 7x3 + 26x2 +44x + 24 = 0
11.
Factor:
2x8 + 5x4y4 – 3y8
Solve.
2x4 + x3 + 2x = 2 – 3x2
12.
Factor:
8x15 + y21
Divide the polynomials using LONG DIVISION =)
÷
13.
(x2 + x – 17)
15.
(3x3 + 11x2 + 4x + 1)
(x – 4)
÷
(x2 + x)
14.
(x3 + 3x2 + 3x + 2)
16.
(4x4 + 5x – 4)
÷
÷
(x – 1)
(x2 – 3x – 2)
Factor the polynomial functions given the following information:
17. f(x) = x3 – 10x2 + 19x + 30
18. f(x) = x3 + 2x2 – 51x + 108
f(6) = 0.
One factor is (x + 9).
19.
f(x) = 3x3 – 4x2 – 28x – 16
x = –2 is a zero.
Factor the polynomial functions.
21. f(x) = x3 – 9x2 + 8x + 60
20.
f(x) = 3x3 – 2x2 – 61x – 20,
5 is a root of the function.
22.
f(x) = 2x3 – 15x2 + 34x – 21
23.
Find all the x-intercepts of the polynomial function.
f(x) = x3 + 5x2 – 4x – 20
24.
Solve the polynomial function.
f(x) = x4 + 4x3 + 7x2 + 16x + 12
25.
Write a polynomial function given its roots: x = 3i, 2 – i.
26.
Write a polynomial function given its roots: x = 1, 3, 2 + 5 .
27.
Find the possible rational roots of: 2x3 – 3x2 + 12
Complete the operations.
28. (x + 5)3
29.
(x + 4) (x2 + 4x – 3)
30.
31.
(x + 4) – (x2 + 4x – 3)
Is the answer in #28 equivalent to
x3 + 125? Explain.
QUICK QUESTIONS
QUESTION
If
3x(x – 2) are factors of a function, find
the zeros.
If
(3x – 1)(6x + 5) are factors of a
2
function, find the zeros.
1
3
If
7
is
a
zero,
what
is
the
factor?
4
If the x-intercept is x = −
1
, what is the
4
factor?
If the x-intercept is x = ±2 3 , what is
5
the factor? If the x-intercept is x = ±6 , what are the
6
factor(s)?
ANSWER
A
ANSWER
B
x=2
x = 0, 2
1 5
x = ,−
3 6
1 5
x=− ,
3 6
(x + 7)
(x – 7)
(4x – 1)
(x –
1
)
4
(x – 2 3 )
(x2 – 12)
(x – 6i)
(x – 6)(x + 6)
(2x + 1)
(2x – 1)
3x2 + 15x + 25
9x2 + 15x + 25
Either 1 or –1
are zeros
All roots are
real numbers
Rational Zero Theorem
Like a Quadratic
11
x4 + 2x3 + 3x + 2
Factor by Grouping
Rational Root Theorem
12
8x3 – 1
Factor by Grouping
Difference of Perfect
Cubes
PRIME
Sum of Perfect Squares
Rational Root Theorem
Factor by Grouping
Factor out the GCF
Like a Quadratic
7
Identify a factor of: 8x3 + 1
8
Identify a factor of: 27x3 – 125
If a the coefficients of a polynomial
9
function add to 0, then what must be
true:
Which method of factoring would you use?
10
x4 + 5x2 + 4
13
x2 + 100
14
x3 + 2x2 – 11x – 12
15
5x4 – 125