Question

Drag each label to the correct location on the table. Each label can be used more than once, but not all labels will be used. Simplify the given polynomials. Then, classify each polynomial by its degree and number of terms.polynormial 1:
`(x - (1)/(2))(6x + 2)`polynormial 2:
`(7 {x}^(2) + 3x) - (1)/(3) (21 { x}^(2) - 12)`polynormial 3:
`4(5 {x}^(2) - 9x + 7) + 2( - 10 {x}^(2) + 18x - 03)`

Answer 1

Given the polynomials, let's simplify the polynomials and label them.

Polynomial 1:

`\begin{gathered} (x-(1)/(2))(6x+2) \\ \text{Simplify:} \\ 6x(x)+2x+6x(-(1)/(2))+2(-(1)/(2)) \\ \\ =6x^2+2x-3x-1 \\ \\ =6x^2-x-1 \end{gathered}`

After simplifying, we have the simplified form:

`6x^2-x-1`

Since the highest degree is 2, this is a quadratic polynomial.

It has 3 terms, therefore by number of terms it is a trinomial.

Polynomial 2:

`\begin{gathered} (7x^2+3x)-(1)/(3)(21x^2-12) \\ \\ \text{Simplify:} \\ (7x^2+3x)-7x^2+4 \\ \\ =7x^2+3x-7x^2+4 \\ \\ \text{Combine like terms:} \\ 7x^2-7x^2+3x+4 \\ \\ 3x+4 \end{gathered}`

Simplified form:

`3x+4`

The highest degree is 1, therefore it is linear

It has 2 terms, therefore by number of terms it is a binomial

Polynomial 3:

`\begin{gathered} 4(5x^2-9x+7)+2(-10x^2+18x-13) \\ \\ \text{Simplify:} \\ 20x^2-36x+28-20x^2+36x-26 \\ \\ \text{Combine like terms:} \\ 20x^2-20x^2-36x+36x+28-26 \\ \\ =2 \end{gathered}`

Simplified form:

`2`

The highest degree is 0 since it has no variable, therefore it is a constant.

It has 1 term, by number of terms it is a monomial.

ANSWER:

Polynomial Simplified form Name by degree Name by nos. of ter

1 6x²-x-1 quadratic Trinomial

2 3x + 4 Linear Binomial

3 2 Constant Monomial