Algebra Examples

$3 x^{2} (x - 1) + - 3 x^{3} + 4 x^{2} - 2 x + 1$

Step 1

Replace all occurrences of $+$ $-$ with a single $-$ . A plus sign followed by a minus sign has the same mathematical meaning as a single minus sign because $1 \cdot - 1 = - 1$

$3 x^{2} (x - 1) - 3 x^{3} + 4 x^{2} - 2 x + 1$

Step 2

A polynomial is a combination of terms separated using $+$ or $-$ signs. Polynomials cannot contain any of the following:

1. Variables raised to a negative or fractional exponent. ( $2 x^{- 2}$ , $x^{\frac{1}{2}}$ , $\dots$ ).

2. Variables in the denominator. ( $\frac{1}{x}$ , $\frac{1}{x^{2}}$ , $\dots$ ).

3. Variables under a radical. ( $\sqrt{x}$ , $\sqrt[3]{x}$ , $\dots$ ).

4. Special features. (trig functions, absolute values, logarithms, $\dots$ ).

Step 3

Determine if the expression breaks any of the rules.

Does not break any of the rules

Step 4

Determine if the expression is a polynomial.

Polynomial