# unit 3 polynomial functions project, algebra homework help

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Unit 3 Project Simplify each expression. 1. 2. 3. 4. (3b)5(8c)3 (7x ­ 2)(x + 4) (6x2 ­ 10x + 4) ­ (x2 + 12x ­ 7) (2x3 + 9x2 ­ 2x + 7) ÷ (x + 2) Factor completely. If the polynomial is not factorable, write prime. 5. 6. 3x3y + x2y2 + x2y 8r3 ­ 64s6 For each function, complete each of the following. a. Graph each function by making a table of values. b. Determine consecutive integer values of x between which each real zero is located. c. Estimate the x­coordinate at which the relative maxima and relative minima occur. 7. 8. g(x) = x3 + 6x2 + 6x ­ 4 h(x) = x4 ­ 2x3 ­ 6x2 + 8x + 5 Solve each equation. 9. 10. p3 + 8p2 = 18p 16x4 ­ x2 = 0 Use synthetic substitution to find f(­2) and f(3). 11. f(x) = 3x4 ­ 12x3 ­ 12x2 + 30x 12. Write the polynomial equation of degree 4 with leading coefficient 1 that has roots at ­2, ­1, 3, and 4. State the possible number of positive real zeros, negative real zeros, and imaginary zeros for each function. 13. 14. f(x) = ­x3 ­ x2 + 14x ­ 24 f(x) = 2x3 ­ x2 + 16x ­ 5 Find all rational zeros of each function. 15. 16. h(x) = x4 + 2x3 ­ 23x2 + 2x ­ 24 f(x) = 5x3 ­ 29x2 + 55x ­ 28 Determine whether each pair of functions are inverse functions. 17. 18. f(x) = 4x ­ 9, g(x) = x 4− 9 f(x) = x 1+ 2 , g(x) = x1 ­ 2 If f(x) = 2x ­ 4 and g(x) = x2 + 3, find each value. 19. 20. (f ­ g)(x) (f • g)(x)
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Unit 3 Project
Simplify each expression.
1.

(3b)5(8c)3

(3b)5(8c)3 = 243b5512c3
= 124416b5c3
2.

(7x - 2)(x + 4)

(7x - 2)(x + 4) = 7x2 – 2x + 28x – 8
= 7x2 + 26x - 8
3.

(6x2 - 10x + 4) - (x2 + 12x - 7)

(6x2 - 10x + 4) - (x2 + 12x - 7) = 5x2 + 2x + 11
4.

(2x3 + 9x2 - 2x + 7) ÷ (x + 2)

(2x3 + 9x2 - 2x + 7) ÷ (x + 2) =
-2

2

2

9 -2 7
-4 -10 24
5 -12 31

Then,
𝟐𝒙𝟐 + 𝟓𝒙 − 𝟏𝟐 +

𝟑𝟏
𝒙+𝟐

Factor completely. If the polynomial is not factorable, write prime.
3x3y + x2y2 + x2y

5.

3x3y + x2y2 + x2y = xy( 3x2+ xy + x)

8r3 - 64s6

6.

8r3 - 64s6 = 8(r3 - 8s6)

For each function, complete each of the following.
a. Graph each function by making a table of values.
b. Determine consecutive integer values of x between which
each real zero is located.
c. Estimate the x-coordinate at which the relative maxima
and relative minima occur.
g(x) = x3 + 6x2 + 6x - 4

7.

a.
x

g(x)

0

-4

1

9

2

40

-1

-5

-2

0

-3

5

-4

4

-5

-9

b. Consecutive integer values of x are: From -6 to -3. From -3 to
0. From 0 to 2.
c. Relative Maxima: x≈-3
Relative Minima: Near to 0

h(x) = x4 - 2x3 - 6x2 + 8x + 5

8.
a.
x

g(x)

-3

62

-2

-3

-1

-6

0

5

1

6

2

-3

3

2

4

69

b. Consecutive integer values of x are: From -3 to -2. From -1 to
0. From 1 to 2. From 2 to 3
c. Relative Maxima: x≈0.5
Relative Minima: x≈-1.5 and x≈2.5

Solve each equation.

9.

p3 + 8p2 = 18p
𝑝3 + 8𝑝2 − 18𝑝 = 0
𝒑(𝒑𝟐 + 𝟖𝒑 − 𝟏𝟖) = 𝟎

Using the zero factor principle:
𝑥=

−𝑏 ± √𝑏 2 − 4𝑎𝑐
2𝑎

For a = 1
b=8
c = -18
−8 + √82 − 4 ∗ 1 ∗ −18
𝑥=
2∗1
𝒙 = √𝟑𝟒 − 𝟒
−8 − √82 − 4 ∗ 1 ∗ −18
𝑥=
2∗1
𝒙 = −√𝟑𝟒 − 𝟒

10.

16x4 - x2 = 0

16x4 - x2 = 0
16x2(x2 - 1) = 0
16x2(x - 1)(x + 1) = 0
So, X1 = X2 = 0
X3 = 1
X4 = -1

Use synthetic substitution to find f(-2) and f(3).
11.

f(x) = 3x4 - 12x3 - 12x2 + 30x

For f(-2)
3(−2)4 − 12(−2)3 − 12(−2)2 + 30(−2) = 36

For f(3)
3(3)4 − 12(3)3 − 12(3)2 + 30(3) = 369

12.

Write the polynomial equation of degree 4...

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