Skill: Identify terms and coefficients in polynomials

A polynomial is made of terms joined by addition or subtraction. To identify each part:

1. Separate the terms at the plus or minus signs.
2. For each term, identify:
   • the coefficient: the number multiplying the variable, including its sign;
   • the variable part: the letter and its exponent;
   • the exponent: the power on the variable.
3. A term with no variable is a constant term.
4. Terms with the same variable part are like terms.

Consider the polynomial

$$3x^2-x+6+2x^2.$$

Step 1: Identify the terms

The terms are

$$3x^2,\qquad -x,\qquad 6,\qquad 2x^2.$$

The minus sign belongs to the term after it, so the second term is $(-x)$, not just $x$.

Step 2: Identify each part

Term	Coefficient	Variable part	Exponent
$(3x^2)$	$3$	$(x^2)$	$2$
$(-x)$	$(-1)$	$x$	$1$
$6$	$6$	none	none
$(2x^2)$	$2$	$(x^2)$	$2$

The coefficient of $(-x)$ is $(-1)$ because a missing coefficient is understood to be $1$, and the negative sign makes it $(-1)$. Also, $x$ means $(x^1)$.

The term $6$ is a constant term because it has no variable.

Finally, $(3x^2)$ and $(2x^2)$ are like terms because they have the same variable part, $(x^2)$. The terms $(-x)$ and $6$ are not like terms with them.