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.”
- 03:14 “So, and the highest power here is 4. Then also, the following are not polinomia. So, whenever you have f of x equals square root of 3 x plus 4 minus 2 x plus 2, is not in polinomia. So, when you have a fraction, polinomi...”
- 24:41 “one is divide Puy-Numia P1 of x equals 2 x squared equals 2 x squared minus 3 x plus 9 by P of 2, P 2 of x equals x plus 3. We have to use lung division method. And find the remainder when x is equal to 3 plus 5 x square...”
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...”
- 09:35 “addition operator. It's a plus sign. Without negative, it is positive. So here we have minus four x. And here, the coefficient is minus four, while this is a constant. Another example, if you have three x plus two, this...”
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.
- 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...”
- 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...”
- 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...”
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...”
- 17:20 “Someone would say, how do we make that possible? Now, the first thing is, let's pick the question. We have the question is x square plus 8x plus 16. Take note of this and take note of this, very, very important. When you...”
- 26:52 “Factorized, P square minus 10P plus 25. The last one says factorized, x square plus xy plus 8x plus y plus 8y plus y plus 8y. So, you could see that I had to bring it into four. So, you could group it into two, two, two....”
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.”
- 08:04 “So that is how to find. So if, for example, in this example and about 2, if you are given, find the quadratic equation. Who's root are, or if you go 1? We have minus 1 and it's minus 1 and it's. So it means our alpha a i...”
- 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...”
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
- 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...”
- 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...”
- 11:22 “that means I'm gonna have X minus five into X plus four equals zero. So when I have that, what comes out is this. In the same vein, I can expand. You can just write for your teacher to know, expand. So your teacher will...”
Solving Linear and Quadratic Equations
This lesson covers the methods for solving simultaneous linear and quadratic equations using substitution. It explains the definitions of linear and quadratic equations and demonstrates how to manipulate these equations to find solutions.
- 20:13 “And here we have negative. So you multiply through by minus one. And this give you y square plus 10 y minus 24 is equals to zero. Multiply true by minus one. Now you cannot factorize. The coefficient of y is one, you hav...”
- 05:03 “it returns to negative, if it is positive. But if it is negative, it returns to positive. Now, factorize. The coefficient of S square is one, and your constant is minus 12. So you are looking for a number that you multip...”
- 14:42 “Some of minus two and minus five will give you minus seven. Substitute this into the equation. There you have X square minus two X minus five X plus 10 is equals to zero. Don't forget your grouping, bring it together. Wh...”