Questions: Classify the following polynomials. Combine any like terms first. x^2 + 3x + 2x - 2x^2 x^3 + 4x - 4x - 4x^2 x^3 + 2x - x^3 - 2x^2 + 3 DONE quadratic trinomial quadratic binomial cubic trinomial cubic binomial

Classify the following polynomials. Combine any like terms first.

x^2 + 3x + 2x - 2x^2

x^3 + 4x - 4x - 4x^2

x^3 + 2x - x^3 - 2x^2 + 3

DONE

quadratic trinomial quadratic binomial cubic trinomial cubic binomial

Transcript text: Classify the following polynomials. Combine any like terms first. \[ \begin{array}{l} x^{2}+3 x+2 x-2 x^{2} \\ x^{3}+4 x-4 x-4 x^{2} \\ x^{3}+2 x-x^{3}-2 x^{2}+3 \end{array} \] DONE $\square$ quadratic trinomial quadratic binomial cubic trinomial cubic binomial

Solution

Solution Steps

Step 1: Combine like terms in the first polynomial

The first polynomial is: \[ x^{2} + 3x + 2x - 2x^{2} \] Combine like terms:

\(x^{2} - 2x^{2} = -x^{2}\)
\(3x + 2x = 5x\)

The simplified form is: \[ -x^{2} + 5x \]

Step 2: Combine like terms in the second polynomial

The second polynomial is: \[ x^{3} + 4x - 4x - 4x^{2} \] Combine like terms:

\(4x - 4x = 0\)
The remaining terms are \(x^{3} - 4x^{2}\)

The simplified form is: \[ x^{3} - 4x^{2} \]

Step 3: Combine like terms in the third polynomial

The third polynomial is: \[ x^{3} + 2x - x^{3} - 2x^{2} + 3 \] Combine like terms:

\(x^{3} - x^{3} = 0\)
The remaining terms are \(-2x^{2} + 2x + 3\)

The simplified form is: \[ -2x^{2} + 2x + 3 \]

Final Answer

The simplified polynomials are: \[ \boxed{ \begin{aligned}

&\quad -x^{2} + 5x \\
&\quad x^{3} - 4x^{2} \\
&\quad -2x^{2} + 2x + 3 \end{aligned} } \]

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