Which of the following monomials can be added to $- 2 x + 4 y + z$ to make the expression a binomial?

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Solution

The correct option is B 2x
The given expression is a trinomial as it has three terms $- 2 x + 4 y and z$
To make this expression a binomial, we need to reduce the number of terms to two.
We can add an existing term with the opposite sign $(2 x o r - 4 y o r - z$ to the )expression to make it binomial.
Example:
$2 x + (- 2 x + 4 y + z) = 4 y + z$

$- 4 y (- 2 x + 4 y + z) = - 2 x + z$

$- z + (- 2 x + 4 y + z) = - 2 x + 4 y$

Of the given options, only 2x fits the requirement.
Hence, adding the monomial $2 x t o - 2 x + 4 y + z$ makes it a binomial.

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