If there is one prayer that you should pray/sing every day and every hour, it is the LORD's prayer (Our FATHER in Heaven prayer)
It is the most powerful prayer. A pure heart, a clean mind, and a clear conscience is necessary for it.
- Samuel Dominic Chukwuemeka

For in GOD we live, and move, and have our being. - Acts 17:28

The Joy of a Teacher is the Success of his Students. - Samuel Dominic Chukwuemeka

Solved Examples on the Theorems of Polynomials

Samuel Dominic Chukwuemeka (SamDom For Peace) Calculators: Calculators for Polynomials
Prerequisites:
(1.) Exponents
(2.) Expressions and Equations
(3.) Relations and Functions

For ACT Students
The ACT is a timed exam...60 questions for 60 minutes
This implies that you have to solve each question in one minute.
Some questions will typically take less than a minute a solve.
Some questions will typically take more than a minute to solve.
The goal is to maximize your time. You use the time saved on those questions you solved in less than a minute, to solve the questions that will take more than a minute.
So, you should try to solve each question correctly and timely.
So, it is not just solving a question correctly, but solving it correctly on time.
Please ensure you attempt all ACT questions.
There is no negative penalty for a wrong answer.

For SAT Students
Any question labeled SAT-C is a question that allows a calculator.
Any question labeled SAT-NC is a question that does not allow a calculator.

For JAMB Students
Calculators are not allowed. So, the questions are solved in a way that does not require a calculator.
Unless specified otherwise, any question labeled JAMB is a question from JAMB Physics

For WASSCE Students: Unless specified otherwise:
Any question labeled WASCCE is a question from WASCCE Physics
Any question labeled WASSCE-FM is a question from the WASSCE Further Mathematics/Elective Mathematics

For NSC Students
For the Questions:
Any space included in a number indicates a comma used to separate digits...separating multiples of three digits from behind.
Any comma included in a number indicates a decimal point.
For the Solutions:
Decimals are used appropriately rather than commas
Commas are used to separate digits appropriately.

Solve all questions.
Show all work.

(1.)


(2.) ACT The function P(x) = x³ − 10x² + 9x − 90, where x is the number of items sold, models the profit P(x), in dollars, for Company A.
The company breaks even when the profit is $0.
How many items must Company A sell to break even?

$ A.\;\; 0 \\[3ex] B.\;\; 3 \\[3ex] C.\;\; 9 \\[3ex] D.\;\; 10 \\[3ex] E.\;\; 90 \\[3ex] $

$ P(x) = x^3 - 10x^2 + 9x - 90 \\[3ex] P(x) = 0 ...to\;\;break\;\;even \\[3ex] \implies \\[3ex] x^3 - 10x^2 + 9x - 90 = 0 \\[3ex] Factor\;\;by\;\;Grouping \\[3ex] x^2(x - 10) + 9(x - 10) = 0 \\[3ex] (x - 10)(x^2 + 9) = 0 \\[3ex] x - 10 = 0 \;\;\;OR\;\;\; x^2 + 9 = 0 \\[3ex] x = 10 \;\;\;OR\;\:\; x^2 = -9 \\[3ex] x = 10 \\[3ex] $ The other value of x is not a real number.
Company A must sell 10 items to break even.
(3.)

(4.)

(5.)

(6.)

(7.)

(8.)

(9.)

(10.)

(11.)

(12.)

(13.)

(14.)

(15.)

(16.)

(17.)

(18.)

(19.)

(20.)





Top




(21.)

(22.)

(23.)

(24.)

(25.)

(26.)

(27.)

(28.)

(29.)

(30.)