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.
- 17:09 “theorem. This is exactly what the remainder theorem is all about. And the theorem is, if the polynomial p of x is divided by x minus a, then the remainder is p of a. The proof is the polynomial function p of x can be wri...”
- 19:35 “Now our theorem we said if p, if the polynomial of p of x is divided by this, then the remainder is what's p of a and our p of a is what is half. Now, a special case of the remainder theorem is when p of x leaves no rema...”
- 17:56 “so if you find your quotient a remainder and you want to find your polynomial back, what we need to do is to multiply your quotient by the divisor, then how do you towards the remainder? It's to give you the polynomial,...”
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...”
- 38:18 “5 in 30 is 6, and of course 5 in 5 is 1, so the final answer is 161, you can also use the other method, you still get the same answer. Right now, the next question is, that one is going to have a remainder.”
- 51:10 “if you do 40 times 9, that's 9 times 4 is 36, we have 360, so I think we can use 9, because if you do 40 times 10, 40 times 10 is 400, I'm 400 is greater than 382, so we're going to use 360, so 40 in 382 is actually 9, s...”