Identify the monomials, binomials and trinomials in the following:
(i) \( 2 x+y-z \)
(ii) \( -2 x^{3} \)
(iii) \( -7-p \)
(iv) \( 5 x y z \)
(v) \( 5-3 y-y^{2} \)
(vi) \( m^{2}-1 \)
To do:
We have to find the monomials, binomials and trinomials from among the given polynomials.
Solution:
Monomials: Polynomials having only one term are known as monomials.
Binomials: A binomial is a polynomial that is the sum of two terms.
Trinomial: A trinomial is a polynomial consisting of three terms.
(i) \( 2 x+y-z \) contains three terms($2x, y, -z$). Therefore, it is a trinomial.
(ii) \( -2 x^{3} \) contains one term($-2x^3$). Therefore, it is a monomial.
(iii) \( -7-p \) contains two terms($-7, -p$). Therefore, it is a binomial.
(iv) \( 5 x y z \) contains one term($5xyz$). Therefore, it is a monomial.
(v) \( 5-3 y-y^{2} \) contains three terms($5, -3y, -y^2$). Therefore, it is a trinomial.
(vi) \( m^{2}-1 \) contains two terms($m^2, -1$). Therefore, it is a binomial.
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