Pattern Matching for Polynomial with Coefficient

[Josh Joubert]

Good day

Working with a gap fill mathematical expression.

For context, this is a high school activity working on developing products in the form of a quadratic trinomial.

I want to match for the product of a monomial and a polynomial with the following specifications:

• form 𝑥(𝑦) where 𝑥 is a monomial and 𝑦 is a polynomial
• 𝑥 may not be omitted or empty
• 𝑥 must be a number, unless it contains any number of variables with or without exponents, in which case it may also contain a number

This is my current pattern:

`+-((($n`?($v^($n)`?)`+)`|($n))((`+-($n`?($v^$n)`+)) + (`+-($n`?($v^($n)`?)`+))`+ + (`+-(($n`?($v^$n)`+)`|$n))))

Which NUMBAS renders as:

From my understanding, the "or number" section (`|($n)) for 𝑥 is causing trouble, though it may also be the quantifiers.

I want the pattern to be able to accept both of the following,

• -3a^2(6a^2-3ab+10ab-5b^2)
• 3(6a^2-3ab+10ab-5b^2)

but NOT:

• 6a^2-3ab+10ab-5b^2

[Christian Lawson-Perfect]

My understanding is you want the expression to be the product of some terms, at least one of which is a monomial.

You might get away with doing something much simpler, by not worrying about exactly what each factor looks like. I think this does what you want:

m_exactly(`!(?+?)`+;monomial * ?`*;other_factors)

The subpattern `!(?+?) is the important bit: it looks for factors which aren't sums. Because you're not capturing the terms of the sum, you don't need the `+- operator. 

So the whole pattern looks for one or more monomial factors, and then allows any number of other factors, which necessarily must be polynomials.

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