Answered

Classify each polynomial as constant, linear, quadratic, or cubic. Combine like terms first.

1. [tex]x^3 - 2x + x^3[/tex]
2. [tex]4x^2 - 6x - 8x^2[/tex]
3. [tex]6x - 6 + 6x[/tex]
4. [tex]5 + 4x^2 - 4x^2 + 5[/tex]

Classify each polynomial as a monomial, binomial, or trinomial. Combine like terms first.

1. [tex]x^3 + 3x^3 + 2x[/tex] [tex]$\square$[/tex]
2. [tex]2x^3 + 5x + 3x^4 - x[/tex] [tex]$\square$[/tex]
3. [tex]4x - 5x + x - 2[/tex] [tex]$\square$[/tex]
4. [tex]6x^2 + 5 - 2x^2 - 9[/tex] [tex]$\square$[/tex]



Answer :

GinnyAnswer
Alright, let's solve this step by step by combining like terms first and then classifying the polynomials by degree and number of terms.

### Classifying by Degree:

1. First Polynomial:
[tex]\[ x^3 - 2x + x^3 \][/tex]

Combine like terms:
[tex]\[ (x^3 + x^3) - 2x = 2x^3 - 2x \][/tex]

The polynomial [tex]\( 2x^3 - 2x \)[/tex] has the highest degree of 3 (cubic).

2. Second Polynomial:
[tex]\[ 4x^2 - 6x - 8x^2 \][/tex]

Combine like terms:
[tex]\[ (4x^2 - 8x^2) - 6x = -4x^2 - 6x \][/tex]

The polynomial [tex]\( -4x^2 - 6x \)[/tex] has the highest degree of 2 (quadratic).

3. Third Polynomial:
[tex]\[ 6x - 6 + 6x \][/tex]

Combine like terms:
[tex]\[ (6x + 6x) - 6 = 12x - 6 \][/tex]

The polynomial [tex]\( 12x - 6 \)[/tex] has the highest degree of 1 (linear).

4. Fourth Polynomial:
[tex]\[ 5 + 4x^2 - 4x^2 + 5 \][/tex]

Combine like terms:
[tex]\[ 5 + 5 + (4x^2 - 4x^2) = 10 \][/tex]

The polynomial [tex]\( 10 \)[/tex] has the highest degree of 0 (constant).

### Classifying by Number of Terms:

1. First Polynomial for Terms:
[tex]\[ x^3 + 3x^3 + 2x \][/tex]

Combine like terms:
[tex]\[ (x^3 + 3x^3) + 2x = 4x^3 + 2x \][/tex]

The polynomial [tex]\( 4x^3 + 2x \)[/tex] contains 2 terms (binomial).

2. Second Polynomial for Terms:
[tex]\[ 2x^3 + 5x + 3x^4 - x \][/tex]

Combine like terms:
[tex]\[ 3x^4 + 2x^3 + 5x - x = 3x^4 + 2x^3 + 4x \][/tex]

The polynomial [tex]\( 3x^4 + 2x^3 + 4x \)[/tex] contains 3 terms (trinomial).

3. Third Polynomial for Terms:
[tex]\[ 4x - 5x + x - 2 \][/tex]

Combine like terms:
[tex]\[ (4x - 5x + x) - 2 = 0x - 2 \][/tex]

The polynomial [tex]\( -2 \)[/tex] contains 1 term (monomial).

4. Fourth Polynomial for Terms:
[tex]\[ 6x^2 + 5 - 2x^2 - 9 \][/tex]

Combine like terms:
[tex]\[ (6x^2 - 2x^2) + (5 - 9) = 4x^2 - 4 \][/tex]

The polynomial [tex]\( 4x^2 - 4 \)[/tex] contains 2 terms (binomial).

### Summary:
#### By Degree:
1. [tex]\( 2x^3 - 2x \)[/tex] is cubic.
2. [tex]\( -4x^2 - 6x \)[/tex] is quadratic.
3. [tex]\( 12x - 6 \)[/tex] is linear.
4. [tex]\( 10 \)[/tex] is constant.

#### By Number of Terms:
1. [tex]\( 4x^3 + 2x \)[/tex]: binomial
2. [tex]\( 3x^4 + 2x^3 + 4x \)[/tex]: trinomial
3. [tex]\( -2 \)[/tex]: monomial
4. [tex]\( 4x^2 - 4 \)[/tex]: binomial

Other Questions