Polynomials and Their Properties
This lesson covers the definition of polynomials and their degrees. It explains how to divide a polynomial by another polynomial of lesser degree and introduces the remainder theorem. Additionally, it discusses how to find factors of polynomials and solve cubic equations using their roots.
- 25:32 “as we have talked about. Thank you for watching. My name is Afiz Alibuk once again. Till next time.”
- 10:41 “then we call it 0's polynomial. We call it what 0 polynomials. Because the value of our x will determine what we want to get. So, I have to go to the minus 2 here. So, minus 2 plus minus 2, minus 2 plus 2, we give us 0....”
- 00:00 “Good day. My name is Adedokun Afeez. I will be taking you furthermath and the topic is Polynomials. At the end of the topic, students will be able to know how to define Polynomials. Define a polinomia by a polinomia of l...”
Simplification of Algebraic Expressions
This lesson covers the definition of algebraic expressions and their components, including terms and coefficients. It explains how to identify like terms, perform arithmetic operations on similar terms, and simplify expressions by inserting or removing brackets.
- 00:02 “Hello. My name is Dorcas Awaye, and today I'll be taking you mathematics. Today we'll be discussing the implication of algebraic expressions. At the end of today's teaching, you should be able to identify and collect lik...”
- 10:21 “So we can easily note which ones are the coefficients. For the variable x, the coefficient is three. For variable y, the coefficient here is plus five. And then we have constant of minus nine. x and y are the variables a...”
- 12:46 “The same thing applies to the second example. The second question, 10 minus x plus two y. So looking at this, the coefficient of y is plus two. The coefficient of x is one. There's an invisible one here. You don't just h...”
Roots of Quadratic Equations
The lesson covers the sum and product of the roots of quadratic equations. It explains how to form a quadratic equation given the sum and product of its roots, and states the conditions for equal roots, real roots, and no roots. The lesson also identifies conditions for a line to intersect or be tan
- 23:11 “Thank you for watching. My name is Adidu Kama-Fiz once again. Till next time.”
- 19:15 “Our a is 1, then c is 9. This is going to be 36 minus 36. So we have 0. So you can see that d equals 0 now. So what type of root are we going to have? We're going to have a real and equal root when we have d equals 0. So...”
- 00:02 “Good day, my name is Adedokun Afeez. I'll be your further maths teacher, and the topic is root of quadratic equation. At the end of the topics, students will be able to know the sum and product of the root of quadratic e...”
Roots of Quadratic Equations
This lesson covers how to find the sum and product of the roots of a quadratic equation. It also explains how to form a quadratic equation given the roots and states the conditions for equal roots, real roots, and no roots. Additionally, it discusses the relationship between a line and a curve in te
- 01:42 “And in our process, I can write X minus alpha equal zero. I can also write X minus beta equal zero. Recall that for roots of a quadratic equation, you can either have one of the factors being equal to zero or both are ze...”
- 09:00 “It's very simple when you have a question to apply it with, so that you can only stand very well. We're gonna try some of this example to actually drive it home and know that you can always form a quadratic equation if y...”
- 13:46 “So for this one, I have X minus two over five, okay, and for this one, I have X equals bigger pardon, X plus one, one number one over two. Equal to zero, equal to zero. One more thing I can do before I bring them togethe...”
Factorization of Algebraic Expressions
This lesson covers the factorization of simple algebraic expressions and quadratic expressions. It includes methods for identifying factors and solving related word problems.
- 13:16 “Then I have plus 2 into 14 is 7 and I have x squared, taking out x to the power 4, will be left with 1, 2x. Oh, beautiful. Now, this has given us a better idea on the factorization process. Which gives you wider view to...”
- 12:30 “So that we will have, what we have, 2x squared, good. 2x squared is common to the 3 of them. That gives us an example to be able to factorize them out. Now, the question is, how do you now rewrite them? How? How do you w...”
- 10:58 “Multiply by x multiplied by x. I have what? 18. I have 18 x with to power 3. That means there are 3 x. Now, what are the possible values? I have 2 multiplied by 3 multiplied by another 3. Now, how many x do we have? 3 x...”
Quadratic Equation and Roots
This lesson covers the formation of quadratic equations from given roots. It explains how to find the sum and product of the roots and demonstrates solving for unknown coefficients in a quadratic equation. Examples are provided to illustrate these concepts.
- 12:42 “the value for B to be -2 we can go ahead to find the value of any roots we are given to find for instance in the example that we want to try saying find the value for find the value for 1 over alpha minus 1 over beta eve...”
- 16:52 “out of it for me if I fix it this one in here look at what I'm going to have or shout instead of writing this alpha squared plus beta squared I'm going to write all these and they fix the product on it so with that is it...”
- 16:01 “this gives me alpha squared plus beta squared over alpha plus beta squared minus I can always take care of this because I know the value of my product to be 3 over 8 but I can still relax and fix it later on so in this c...”
Basic Operations on Whole Numbers
This lesson covers addition and subtraction of whole numbers, including how to align numbers by their place values. It also explains multiplication and division by 10, 100, and 1000, and introduces the use of the BODMAS rule for solving mixed operations.
- 39:05 “So, since you have a question, you don't need a remainder. Okay, now question, so now we have, that's the next question, question C, it does a 1, 4, 5. 1, 4, 5 divided by charging. Now, this one is going to have a remain...”
- 01:05:43 “5 times 0 is 0, 5 times 5 is 25, 5 times 3 is 15, 15 plus 2, you get 17, so you have 17 here, 2 times 0 is 0, 2 times 0 is 0, 2 times 5 is 10, you write 0, you carry 1, then 2 times 3 is 6 plus 1 is 7, so you have 7 here...”