I wanted to understand what a quadratic trinomial is–and why it’s called that. I looked for a definition of “quadratic” and got this from Merriam-Webster:

involving terms of the second degree at most

Based on what I read at some other sites, I assume “second degree” means that one of the terms (monomials?) has to be squared…although according to this definition, it sounds like it need not be. That is, a quadratic expression can’t have a monomial that exceeds being squared. (My guess is that this is wrong, but then the M-W definition seems inaccurate or poorly written.)

For “trinomial,” I found a site (mathplanet) that first talked about monomials and polynomials. I’m not sure about the trustworthiness of the site, but here’s what it said:

A monomial is a number, a variable or a product of a number and a variable where all exponents are whole numbers.

These numbers are examples: 42,5x,14x^{12},2pq

but these examples are not: 4+y,5/y,14^{x}, 2pq^{−2}

(I’m guessing 14_{x} is not a monomial because “x” might not be a whole number?)

Polynomials would just be a sum of monomials. (What could a polynomial be a produce to monomials? If you multiplied monomials that would just lead to a monomial? What if you divided them?)

Based on what I read at some other sites, I assume “second degree” means that one of the terms (monomials?) has to be squared…

Second degree means with a power of 2, yes.

although according to this definition, it sounds like it need not be. That is, a quadratic expression can’t have a monomial that exceeds being squared. (My guess is that this is wrong, but then the M-W definition seems inaccurate or poorly written.)

That does seem to be what it means, but I’m trying to think of why. One explanation might be like the relationship between squares and rectangles: all squares are rectangles, but not all rectangles are squares. Is it possible that all linear equations are quadratic as well? I’ve never heard this.

(I’m guessing 14ₓ is not a monomial because “x” might not be a whole number?)

I think there may have been an error in your copying and pasting, because the subscript x has a ton of possible meanings. The superscript x — hm. I have to think about this.

Polynomials would just be a sum of monomials.

Yes. So binomials and trinomials are also polynomials, just specific kinds.

(What could a polynomial be a produce to monomials?

I think I need you to restate the question.

If you multiplied monomials that would just lead to a monomial? What if you divided them?)

Yes and the same thing.

Remember, multiplication and division are essentially the same thing. X times .5 is the same thing as X divided by 2. So multiplying 2x by 2 would give you x, which is a monomial, as long as you’re not dividing by 0 anywhere.

One explanation might be like the relationship between squares and rectangles: all squares are rectangles, but not all rectangles are squares. Is it possible that all linear equations are quadratic as well? I’ve never heard this.

What exactly is a linear equation, versus other equations? Also, I’m still not sure why a quadratic equation is called quadratic…because the equation has a squared monomial?

The superscript x — hm. I have to think about this.

Yeah, it was supposed to be a superscript.

What could a polynomial be a produce to monomials?

My goodness that’s awful! I think I meant to ask why multiplying monomials wouldn’t also be a polynomial.

So multiplying 2x by 2 would give you x, which is a monomial, …

I have a question about factorizing related to the two of the problems below:

1. ab

^{2}+a^{2}bAnswer: ab(b+a)

and

2. ax

^{3}+ax^{2}Answer: ax

^{2}(x+1)Here’s what I’m wondering:

When you see “ab

^{2}” that is a(b^{2}), not ab(ab). ab(ab) would equal a^{2}b^{2}, right?That’s right. The exponent only applies to the term immediately preceding it unless there are parentheses.

OK, thanks.

I wanted to understand what a quadratic trinomial is–and why it’s called that. I looked for a definition of “quadratic” and got this from Merriam-Webster:

Based on what I read at some other sites, I assume “second degree” means that one of the terms (monomials?) has to be squared…although according to this definition, it sounds like it need not be. That is, a quadratic expression can’t have a monomial that exceeds being squared. (My guess is that this is wrong, but then the M-W definition seems inaccurate or poorly written.)

For “trinomial,” I found a site (mathplanet) that first talked about monomials and polynomials. I’m not sure about the trustworthiness of the site, but here’s what it said:

These numbers are examples: 42,5x,14x

^{12},2pqbut these examples are not: 4+y,5/y,14

^{x}, 2pq^{−2}(I’m guessing 14

_{x}is not a monomial because “x” might not be a whole number?)Polynomials would just be a sum of monomials. (What could a polynomial be a produce to monomials? If you multiplied monomials that would just lead to a monomial? What if you divided them?)

Second degree means with a power of 2, yes.

That does seem to be what it means, but I’m trying to think of why. One explanation might be like the relationship between squares and rectangles: all squares are rectangles, but not all rectangles are squares. Is it possible that all linear equations are quadratic as well? I’ve never heard this.

I think there may have been an error in your copying and pasting, because the subscript x has a ton of possible meanings. The superscript x — hm. I have to think about this.

Yes. So binomials and trinomials are also polynomials, just specific kinds.

I think I need you to restate the question.

Yes and the same thing.

Remember, multiplication and division are essentially the same thing. X times .5 is the same thing as X divided by 2. So multiplying 2x by 2 would give you x, which is a monomial, as long as you’re not dividing by 0 anywhere.

What exactly is a linear equation, versus other equations? Also, I’m still not sure why a quadratic equation is called quadratic…because the equation has a squared monomial?

Yeah, it was supposed to be a superscript.

Oops sorry. I meant dividing 2x by 2 would give you x, a monomial.

OK, got it.