You can put this solution on YOUR website! A polynomial of degree 4 will have 4 zeros. The zero of 3 with a multiplicity of 2 counts as two of these zeros.
Factoring special products Video transcript We need to factor 25x to the fourth minus 30x squared plus 9. And this looks really daunting because we have something to the fourth power here.
And then the middle term is to the second power.
But there's something about this that might pop out at you. And the thing that pops out at me at least is that 25 is a perfect square, x to the fourth is a perfect square, so 25x to the fourth is a perfect square.
And 9 is also perfect square, so maybe this is the square of some binomial. And to confirm it, this center term has to be two times the product of the terms that you're squaring on either end.
Let me explain that a little bit better So, 25x to the fourth, that is the same thing as 5x squared squared, right?
So it's a perfect square.
It could be either one. Now, what is 30x squared? What happens if we take 5 times plus or minus 3? So remember, this needs to be two times the product of what's inside the square, or the square root of this and the square root of that.
Given that there's a negative sign here and 5 is positive, we want to take the negative 3, right? That's the only way we're going to get a negative over there, so let's just try it with negative 3.
So what is what is 2 times 5x squared times negative 3?
Well, 2 times 5x squared is 10x squared times negative 3. It is equal to negative 30x squared. We know that this is a perfect square.
So we can just rewrite this as this is equal to 5x squared-- let me do it in the same color. And we saw in the last video why this works. And if you want to verify it for yourself, multiply this out.
You will get 25x to the fourth minus 30x squared plus 9.Using these notations we write the nth degree Taylor Polynomial for f (x) Be sure you understand what the next several terms would like for this example and for others we have Exercise Find the 10th degree Taylor Polynomial centered at x = a for the given functions: (a) sin(x),atx = π/2 (b).
May 21, · This video explains how to find all of the zeros of a degree 3 polynomial function and how to write the function as a product of linear factors. Page 7 ____ 23 Using the polynomial, f(x)= 2x 3 +4x−8, explain how the degree and leading coefficient will effect the end behavior. A Because the degree is odd, .
Jan 12, · Best Answer: 4x⁴ + 6x³ - 2 - x⁴ = (4x⁴ - x⁴) + 6x³ - 2 = 3x⁴ + 6x³ - 2 Fourth degree (also called quartic) Three terms (trinomial) 9x² – 2x + 3x² Status: Resolved.
Sep 20, · Edit Article How to Factor a Cubic Polynomial. In this Article: Article Summary Factoring By Grouping Factoring Using the Free Term Community Q&A This is an article about how to factorize a 3 rd degree polynomial.
We will explore how to factor using grouping as well as using the factors of the free term%(). Page 1 of 2 Chapter 6 Polynomials and Polynomial Functions POLYNOMIAL MODELING WITH TECHNOLOGY In Examples 1 and 3 you found a cubic model that exactly fits a set of data points. In many real-life situations, you cannot find a simple model to fit data points exactly.