Identifying constant terms in expressions

[Probability]

I thought I had this in good understanding but I've had my legs kicked from under me on this example. An expression such as;

[MATH]{3}{p}{q}-{2}+5{p^2}[/MATH] has one constant term, namely [MATH]-{2}[/MATH]
The book does not mention square roots in the discussion but asked the question, identify the constant terms in;

[MATH]{2x}+{5}\sqrt{2}+{x^2}[/MATH]
So I answered the expression by writing [MATH]{5}[/MATH] which I clearly got wrong!

So the [MATH]\sqrt{2}[/MATH] is that then multiplied by [MATH]{5}={7.1}[/MATH] but written as [MATH]{5}\sqrt{2}[/MATH] as the answer.

All I'm asking is, should a constant term in conjunction with a square root be thought of as being the constant term and written as [MATH]{5}\sqrt{2}[/MATH]

 

[Deleted member 4993]

I thought I had this in good understanding but I've had my legs kicked from under me on this example. An expression such as;

[MATH]{3}{p}{q}-{2}+5{p^2}[/MATH] has one constant term, namely [MATH]-{2}[/MATH]
The book does not mention square roots in the discussion but asked the question, identify the constant terms in;

[MATH]{2x}+{5}\sqrt{2}+{x^2}[/MATH]
So I answered the expression by writing [MATH]{5}[/MATH] which I clearly got wrong!

So the [MATH]\sqrt{2}[/MATH] is that then multiplied by [MATH]{5}={7.1}[/MATH] but written as [MATH]{5}\sqrt{2}[/MATH] as the answer.

All I'm asking is, should a constant term in conjunction with a square root be thought of as being the constant term and written as [MATH]{5}\sqrt{2}[/MATH]

Value of √2 does NOT change - like value of 4 or 37 or (37*4 =)148 does not change. Those are all constants.

Thus value of (5*√2 =) 5√2 does not change - it is a constant.

 

[Steven G]

First, 5*sqrt(2) is Not 7.1

2nd, 5 is NOT a term. Terms are separated by + and - signs not inside parenthesis. The terms 2x, 5sqrt(5) and x^2

 

[HallsofIvy]

To clarify Jomo's first point: \(\displaystyle 5\sqrt{2}\) is, using a calculator, approximately 7.0710678118654752440084436210485 and another approximation, to only one decimal place so not as good, is 7.1 but those are just approximations. The only way to write an exact value is \(\displaystyle 5\sqrt{2}\).

However you write it, \(\displaystyle 5\sqrt{2}\) is a single number. It is the "constant term" in that polynomial.

 

[lev888]

I thought I had this in good understanding but I've had my legs kicked from under me on this example. An expression such as;
[MATH]{3}{p}{q}-{2}+5{p^2}[/MATH] has one constant term, namely [MATH]-{2}[/MATH]

I think the first step in this process should be identifying the variable. Since constant terms can be represented by numbers and letters we don't really know which ones are constant until we know which letter(s) represent the variable(s) (I think the author of the problem should make it clear).
In your example above -2 is the constant if p is the variable. What if q is the only variable? Then 5p² is also a constant term, since it does not change if q changes.

 

[Probability]

I think the first step in this process should be identifying the variable. Since constant terms can be represented by numbers and letters we don't really know which ones are constant until we know which letter(s) represent the variable(s) (I think the author of the problem should make it clear).
In your example above -2 is the constant if p is the variable. What if q is the only variable? Then 5p² is also a constant term, since it does not change if q changes.

In this particular example the [MATH]{-2}[/MATH]is as you say the constant term. The author says, if on the other hand, a term is of the form, "A number x a combination of letters", then the number is called the coefficient of the term, and the author says that the term is a term in whatever the combination of letters is. So in this information, not correctly understood at the time by me, it is probably including the square roots.

 

[lev888]

In this particular example the [MATH]{-2}[/MATH]is as you say the constant term. The author says, if on the other hand, a term is of the form, "A number x a combination of letters", then the number is called the coefficient of the term, and the author says that the term is a term in whatever the combination of letters is. So in this information, not correctly understood at the time by me, it is probably including the square roots.

The coefficient is not the number, it's whatever is not the variable part of the term. If x is the only variable, then in 2ax the coefficient is 2a, not 2.

 

[Probability]

The coefficient is not the number, it's whatever is not the variable part of the term. If x is the only variable, then in 2ax the coefficient is 2a, not 2.

Sorry I've just realised that you might be misunderstanding what I wrote here; "A number x a combination of letters". The 'x' here was meant to reflect the understanding of multiplication and not a variable.

 

[JeffM]

The coefficient is not the number, it's whatever is not the variable part of the term. If x is the only variable, then in 2ax the coefficient is 2a, not 2.

To elaborate briefly, when discussing the general quadratic function

[MATH]ax^2 + bx + c[/MATH], we frequently call c the constant term.

The justification for that is that we are generalizing things like

[MATH]3x^2 +2x - 1[/MATH], where 1 clearly is an invariant value.

All of this suggests to me that we really need to teach and use a consistent vocabulary such as "number," "numeral," "pronumeral," "parameter," "unknown," and "variable."

[MATH]5 \sqrt{2}[/MATH] is an exact number and a constant but it is not a numeral because it is not made up exclusively of digits and an implied or explicit radix point. I suspect that the OP is hazy on the distinctions between numerals and numbers and between numerals and constants.

 

[lev888]

Sorry I've just realised that you might be misunderstanding what I wrote here; "A number x a combination of letters". The 'x' here was meant to reflect the understanding of multiplication and not a variable.

No, I understood that x meant multiplication. So what I wrote stands, with clarification from the post #9.

 

[Probability]

First, 5*sqrt(2) is Not 7.1

2nd, 5 is NOT a term. Terms are separated by + and - signs not inside parenthesis. The terms 2x, 5sqrt(5) and x^2

Now I know where I've see you before Jomo

Is it Johann Carl or Friedrich Gauss (1777 - 1855) Your looking quite good for your age

Oh yes I'll expect you to be at the top of your class when I get to inequalities

 

[Steven G]

Friedrich Gauss, actually Dr. Sir Friedrich Gauss.