Match the description with the most appropriate algebraic...

Match the description with the most appropriate algebraic expression from the column on the right. ____An expression with three terms that is not a trinomial a) $8 x^{3}+\frac{2}{x^{2}}$ b) $5 x^{4}+3 x^{3}-4 x+7$ c) $\frac{3}{x}-6 x^{2}+9$ d) $8 t-4 t^{5}$ e) 5 f) $6 x^{2}+7 x^{4}-2 x^{3}$ g) $4 t-2 t^{7}$ h) $3 t^{2}+4 t+7$

Match the description with the most appropriate algebraic expression from the column on the right.
____An expression with three terms that is not a trinomial

a) $8 x^{3}+\frac{2}{x^{2}}$
b) $5 x^{4}+3 x^{3}-4 x+7$
c) $\frac{3}{x}-6 x^{2}+9$
d) $8 t-4 t^{5}$
e) 5
f) $6 x^{2}+7 x^{4}-2 x^{3}$
g) $4 t-2 t^{7}$
h) $3 t^{2}+4 t+7$

Key Concepts

Non-Polynomial Expressions

Expressions that appear to have multiple terms but include variables with negative or fractional exponents are not considered polynomials. Even if there are three terms present, the presence of a term such as a variable in the denominator (which implies a negative exponent) disqualifies the expression from being a trinomial.

Trinomial

A trinomial is a specific kind of polynomial that contains exactly three terms. The classification strictly applies when each term adheres to the polynomial form with nonnegative integer exponents.

Polynomial

A polynomial is a type of algebraic expression that consists of a finite sum of terms, where each term is a constant multiplied by a variable raised to a nonnegative integer exponent. This restriction on the exponent is critical in defining the expression as a polynomial.

Algebraic Expression

An algebraic expression is a mathematical phrase that can include numbers, variables, and operation symbols. It represents a combination of terms that can be manipulated using algebraic rules and can include terms that are constants, variables raised to powers, or products of these.

Transcript

00:01 Okay, so this question says that we need three terms, but this is not a polynomial.

00:16 So not a polynomial.

00:19 I'm just going to call it poly.

00:22 So a polynomial, just as a reminder, these are the ones that have a x to some power, we'll call it n.

00:32 Is just a constant.

00:34 X is our variable and n is some power plus bx and we'll call this one n1 and this n2 and we can just keep going until we have really as far as we want we'll just call this alpha x just to the and and we'll just call it alpha well that's probably a little confusing but really what we're saying is we just have all of these things for example we could have like 3x squared plus 3x plus that would be a polynomial or and these these exponents could get as high as they want as long as they're they're natural numbers.

01:41 So we don't want any like fractions or things like that.

01:45 So what we want is we want three terms, but we don't want it to be in this form.

01:52 So that would mean that we have something like, like maybe a square root in here, x plus three inside of the square root, plus two plus x.

02:11 Something like this this is not a power of n and so that would be a clear thing or things like that another thing that doesn't work is if x is in the denominator so so if we come down and make a little bit more room here if x is in the denominator it also doesn't work so this is like if we have a 3 over x plus 2 plus x or something like this um these are not polynomials when whenever x is in the denominator um it's not it's not a polynomial so this is we're going to have some unique case like this where we we don't have the generic form um ax to some power and another constant times x to some power.

03:13 So as we look down our list that they provide us, there's two of them that don't have this common pattern of some number times x to a power or even just a number by itself works.

03:29 We've been using that in our examples when i've said like plus 2 plus x or things like that.

03:36 So these two ones that we have to decide between is we have ax cubed plus 2 over x squared.

03:51 So this is letter a...

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