No.101 Monomials and Polynomials

POINT

A monomial is an expression consisting only of a product of numbers and variables, and a polynomial is a sum of monomials.

Example

\(\frac{1}{4}a,\quad 3a-2b+1,\quad 5x^2y\)

① Choose the polynomial.

② Write the terms of the polynomial in ①.

③ Give the coefficients of the terms containing variables in ①.

① Polynomial: \(3a-2b+1\)
② Terms: \(3a,\ -2b,\ 1\)
③ Coefficient of \(a\): \(3\); coefficient of \(b\): \(-2\)

Try it yourself.

For each set, choose the polynomial, write its terms, and give the coefficients of the terms containing variables.

PRACTICE 01

\(4x+y-2,\quad \frac{2}{3}x,\quad 3ab^2\)

Polynomial: \(4x+y-2\) (terms: \(4x,\ y,\ -2\); coefficients of variable terms: \(4,\ 1\))

PRACTICE 02

\(-5a,\quad 7xy\quad a^2+2a-1,\)

Polynomial: \(a^2+2a-1\) (terms: \(a^2,\ 2a,\ -1\); coefficients of variable terms: \(1,\ 2\))

PRACTICE 03

\(5a,\quad 2a-b,\quad -3x^2y\)

Polynomial: \(2a-b\) (terms: \(2a,\ -b\); coefficients: \(2,\ -1\))

PRACTICE 04

\(x+y+1,\quad 7xy,\quad -\frac12m\)

Polynomial: \(x+y+1\) (terms: \(x,\ y,\ 1\); coefficients: \(1,\ 1\))

PRACTICE 05

\(4p^2q,\quad 6\quad 3p-2q,\)

Polynomial: \(3p-2q\) (terms: \(3p,\ -2q\); coefficients: \(3,\ -2\))

PRACTICE 06

\(-2ab,\quad a^2+b^2-3,\quad \frac35x\)

Polynomial: \(a^2+b^2-3\) (terms: \(a^2,\ b^2,\ -3\); coefficients of variable terms: \(1,\ 1\))