3:09 “2x” IS a polynomial? That single term qualifies to be called a polynomial? And “2x + 7” is also a polynomial? And so is “2x squared + 7x + 6”? All three of these terms qualify as polynomials? Even the first one, which is just one single term? And, that one term, “2x”which is a polynomial, is also a monomial? A monomial lies underneath the umbrella term of the polynomial?
@@raymondruiz5839 Yes, I know “poly” means many. But does he not say that “2x” is a polynomial? But it’s only one term? It’s not many? That’s why am asking for clarification. Is it a polynomial because the term itself contains two elements, the coefficient and the variable? That’s two things. Does two of something constitute many?
@@johnparadise3134 Polynomials consist of the sums and differences of monomials so the 2x mononomial on its own could be considered its own sum making it a polynomial?? That's the only way I could make sense of that part.
you can write 2x as 2x+0 If you follow the formal definition of a polynomial even (x-1)(x+8) is a polynomial because it can be written as x^2+7x-8. The word polynomial does not refer to the way the expression has been written but to the fact that the expression can be written in a specific form. That's why (x-1)(x+8) is also called a polynomial, as can be found in many good books about calculus. Even 0 is considered as a polynomial, the so called zero polynomial.
And again one error more than in my previous comment: at 15.57 you say that a 5th degree ploynomial has max 4 terms. What about x^5 + 3x^4 + x^3 - 6x^2 + x - 5. There are 6 terms! And another error: at 14:52. yoy say that if we have a 3rd degree polynomial (x+5)(x-3)(x-7) is that 3rd degree polynomial. Oh? And what about 8(x+5)(x-3)(x-7). or 3(x+5)(x-3)(x-7). also 3rd degree polynomials with the same roots -5, 3 and 7. So why do you say that (x+5)(x-3)(x-7). is "the" polynomial? By the way: you call the graph a 3rd degree polynomial and that's also wrong. The polynomial is the third degree expression (function) and it is not the same as the graph. Please stop teaching the wrong things.
And again: please stop with this nonsense! A 4th degree polynomial has 4 solutions? A polynomial has no solutions! Setting a polynomial equal to 0 creates an equation and the equation has solutions. Please stop telling us that a polynomial has solutions. In this way students will use the word solution in an incorrect way and may fail for exams. Please teach students what math is really about. And another remark: you state that a 4th degree polynomial has 4 "solutions". So what are the 4 solutions of x^4=0? That equation has only 1 solution. Of course you can discuss the graphical situation at the point with x=0 when you make a graph, but nevertheless the equation x^4=0 has 1 an only 1 solution, despite what you tell us about a 4th degree polynomial. Note: the fact that you graph the 4th degree function the way you do means that you restrict to real values for x. So it is even possible that in your situation a 4th degree function does not have any "what you call solutions" at all.
Thank you for explaining Polynomials The Big Picture in basic and advanced mathematics.
But see my comments for the errors he makes.
It's an excellent lecture to understand what polynomials are. Thank you so much.
But see my comments for the errors he makes.
Thank you so much
But see my comments for the errors he makes.
Wonderful lesson but beyond my standard
3:09 “2x” IS a polynomial? That single term qualifies to be called a polynomial? And “2x + 7” is also a polynomial? And so is “2x squared + 7x + 6”? All three of these terms qualify as polynomials? Even the first one, which is just one single term? And, that one term, “2x”which is a polynomial, is also a monomial? A monomial lies underneath the umbrella term of the polynomial?
Poly=many, therefore many terms
@@raymondruiz5839
Yes, I know “poly” means many. But does he not say that “2x” is a polynomial? But it’s only one term? It’s not many? That’s why am asking for clarification. Is it a polynomial because the term itself contains two elements, the coefficient and the variable? That’s two things. Does two of something constitute many?
@@johnparadise3134 Polynomials consist of the sums and differences of monomials so the 2x mononomial on its own could be considered its own sum making it a polynomial?? That's the only way I could make sense of that part.
you can write 2x as 2x+0
If you follow the formal definition of a polynomial even (x-1)(x+8) is a polynomial because it can be written as x^2+7x-8. The word polynomial does not refer to the way the expression has been written but to the fact that the expression can be written in a specific form. That's why (x-1)(x+8) is also called a polynomial, as can be found in many good books about calculus. Even 0 is considered as a polynomial, the so called zero polynomial.
And again one error more than in my previous comment:
at 15.57 you say that a 5th degree ploynomial has max 4 terms. What about x^5 + 3x^4 + x^3 - 6x^2 + x - 5. There are 6 terms!
And another error:
at 14:52. yoy say that if we have a 3rd degree polynomial (x+5)(x-3)(x-7) is that 3rd degree polynomial. Oh? And what about 8(x+5)(x-3)(x-7). or 3(x+5)(x-3)(x-7). also 3rd degree polynomials with the same roots -5, 3 and 7. So why do you say that (x+5)(x-3)(x-7). is "the" polynomial?
By the way: you call the graph a 3rd degree polynomial and that's also wrong. The polynomial is the third degree expression (function) and it is not the same as the graph.
Please stop teaching the wrong things.
And again: please stop with this nonsense! A 4th degree polynomial has 4 solutions? A polynomial has no solutions! Setting a polynomial equal to 0 creates an equation and the equation has solutions. Please stop telling us that a polynomial has solutions. In this way students will use the word solution in an incorrect way and may fail for exams. Please teach students what math is really about. And another remark: you state that a 4th degree polynomial has 4 "solutions". So what are the 4 solutions of x^4=0? That equation has only 1 solution. Of course you can discuss the graphical situation at the point with x=0 when you make a graph, but nevertheless the equation x^4=0 has 1 an only 1 solution, despite what you tell us about a 4th degree polynomial.
Note: the fact that you graph the 4th degree function the way you do means that you restrict to real values for x. So it is even possible that in your situation a 4th degree function does not have any "what you call solutions" at all.