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Is the sum of two trinomials always a trinomial? Explain why or why not.

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Algebra

Chapter 5

Exponents and Polynomials

Section 5

Adding and Subtracting Polynomials

Polynomials

Campbell University

Oregon State University

Harvey Mudd College

Lectures

00:58

Will the sum of two trinom…

00:48

Use a graphing calculator …

00:33

Explain why the product of…

01:27

When two binomials are add…

01:05

a. Is the sum of two polyn…

01:23

Explain what it means when…

03:37

Can a quadratic expression…

03:41

Complete the statement wit…

If the terms of a polynomi…

01:06

Many times, multiplying tw…

01:39

A polynomial is factorable…

00:49

What is a trinomial? Give …

01:18

In the factoring of a trin…

01:17

Reasoning Is the product o…

00:56

Is the sum of two rational…

01:07

Explain how it is possible…

01:43

When factoring a trinomial…

In your own words, explain…

00:32

Is 2 a factor of the expre…

00:01

Is the product of a monomi…

So in this problem, they're asking us to determine if the sum of two try no meals is always going to be a trying a wheel. Remember, try no meal is a polynomial with three terms, and the answer in this case is that it's not always going to be a try. No meal. And here's why. For example, let's say I had the China meal Hey X to the fourth plus six x to the third plus four X Square. And let's say I add that to the China meal. Ah seven x to the third plus five x squared, plus tax. Well, if I was to go and add these to Paulina Muse to each other because it's addition, being essentially dropped both of the exponents and then combine their light terms. So our light terms Let's start with our first term. We have eight X to the fourth. There is no over eight exit before, so we'll just bring it down as eight x to the fourth. Our next term is six X to the third. Well, there's also a positive seven extra third, so we'll have plus six x to the third plus seven x to the third. Our next term is for X squared. It also has a like term, a positive five x word. So I plus four x squared plus five x squared. And if you know this are only term that has been accounted for, is positive a Dex, but it also does not have a life term. So we'll have plus a tax. Well, let's now go ahead and combine our July terms like we are re mentioned. Eight extra. The fourth does not have a life term, so that will stay the same eight x to the fourth. Now, if you look at our extra third terms, we have six sex to the 30 plus seven x to the third Well, six plus seven is 13 so we'll have plus 13 x to the third. Now let's combine our X squared terms we have for X Square plus five X word. Well, four plus five is equal to nine. So a plus nine x squared and we already mentioned a vexes all have, like, time like term. Still, just bring that down. So if you know this, we started out by adding to try no meals. But our final answer has four terms. Therefore, there's not a try. No meal. So their fourth e answer is no. When you add to try no meals, you do not necessarily get a try no meal.

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00:50

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02:31

$$\text { Factor: } 6 x^{4 m} y^{n}+21 x^{3 m} y^{2 n}-15 x^{2 m} y^{3 n…

01:03

Factor completely.$$x^{2}(y+1)-3 x(y+1)-70(y+1)$$

00:59

Choose the correct method from Section 6.1, Section 6.2, Section 6.3, or Sec…

01:10

Multiply.$$(x-8)\left(x^{3}-4 x^{2}-2 x-2\right)$$

02:04

Perform each division. See Example 5.PROBLEM CANNOT COPY

00:52

Multiply.$$\left(4 a-\frac{5}{4} r\right)\left(4 a+\frac{3}{4} r\rig…

Evaluate each expression for $x=6 .$ See Example 1.$$\frac{-x+1}{x^{…

00:55

Divide, and then simplify, if possible.$\frac{r^{2}+12 r+11}{r} \div \fr…

00:14

Subtract and simplify the result, if possible.$\frac{2-7 n}{n^{2}+5}-\fr…