Geometry formula list

Graded Assignment
Unit Test, Part 2: Polynomials and Power Functions
Answer the questions and show your work. When you are finished, submit this assignment to your teacher through the appropriate dropbox basket.
(3 pts)
1.) Factor
100x^2 – 49 to factor, use the difference of squares formula, because both the terms are perfect squares the difference of squares formula is a^2 – b^2 = (a-b)(a+b) therefore 100x^2 – 49 = (10x)^2 – 7^2 = (10x – 7)(10x +7)

(5 pts)
2.) Solve x^2 – 11x = -30
(x^2 – 11x) + 30 = -30 +30 x^2 – 11x +30 = 0
Reorder the terms:
30 + 11x + x2 = 0

Solving
30 + 11x + x2 = 0

Factor a trinomial.
(6 + x)(5 + x) = 0

Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6 x = 0 + -6

Combine like terms: 0 + -6 = -6 x = -6

Simplifying x = -6
Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5 x = 0 + -5

Combine like terms: 0 + -5 = -5 x = -5

Simplifying x = -5
Solution
x = {-6, -5}

(12 points)
3.) For the function f(x) = x3 – 16x, do the following:
a. Complete the table of values below.
b. Sketch the function on the coordinate plane.
c. Describe the function’s end behavior.
d. Factor the function completely.

a. x –2
–1
0
1
2 f(x) 24
15
0
-15
-24

b. The function is cubic(squared)

c. End behavior: the graph falls to the left and rises to the right

d. Factor completely: x(x² -16) = 0

Next factorise difference of squares
(x² -16) = (x + 4)(x - 4)

x(x + 4)(x - 4) = 0......... now put each equal to zero as a zero multiplying will give a zero result

so x could be zero x = 0
(x + 4) = 0..............x = -4
(x - 4) = 0..............x = + 4
Results are x = -4, 0 and +4