Questions: Which terms can be combined in the polynomial (x^4+6 x^2-5 x+2 x^3-9 x^2 ?) constant linear quadratic cubic

Transcript text: Which terms can be combined in the polynomial $x^{4}+6 x^{2}-5 x+2 x^{3}-9 x^{2} ?$ $\square$ constant linear quadratic cubic

Solution

Solution Steps

To combine like terms in the polynomial, we need to group terms with the same degree. The degrees of the terms are determined by the exponent of $ x $.

Solution Approach

Identify and group the terms with the same degree.
Combine the coefficients of the grouped terms.

Step 1: Identify and Group Like Terms

We start with the polynomial: \[ x^4 + 6x^2 - 5x + 2x^3 - 9x^2 \]

Step 2: Combine Like Terms

Group the terms with the same degree:

$ x^4 $ (degree 4)
$ 2x^3 $ (degree 3)
$ 6x^2 - 9x^2 = -3x^2 $ (degree 2)
$ -5x $ (degree 1)

Step 3: Write the Simplified Polynomial

Combine the grouped terms to get the simplified polynomial: \[ x^4 + 2x^3 - 3x^2 - 5x \]

Final Answer

The simplified polynomial is: \[ \boxed{x^4 + 2x^3 - 3x^2 - 5x} \]

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