Question

Please help do not give me answers on the internet

Answer 1

Given:

The measures of the sides of the rectangle are (2x+7) and (5x+9).

Aim:

We need to find the area of the given rectangle.

Step-by-step explanation:

A)

Let the length of the rectangle, l=2x+7.

Let the width of the rectangle, w =5x+9.

Consider the formula to find the area of the rectangle.

`A=l* w`

Substitute l=2x+7 and w =5x+9 in the formula.

`A=(2x+7)*(5x+9)`

Multiply (2x+7) and (5x+9) as follows.

`A=2x*(5x+9)+7*(5x+9)`

`A=(2x*5x)+(2x*9)+(7*5x)+(7*9)`

`A=10x^2+18x+35x+63`

`A=10x^2+53x+63`

Answer:

`\text{ The area of the rectangle is }10x^2+53x+63.`

B)

`10x^2+53x+63`

Here variable is x and the highest power of the variable x is 2.

We know that the highest power of the variable is degree.

`degree\text{ =2.}`

This expression contains three terms.

We know that an algebraic expression containing three terms is trinomial.

`10x^2+53x+63\text{ is trinomial.}`

Answer:

`degree\text{ =2.}`
`10x^2+53x+63\text{ is trinomial.}`

C)

Consider the polynomials (2x+7) and (5x+9).

`\text{ The multiplication of \lparen2x+7\rparen and \lparen5x+9\rparen is }10x^2+53x+63.`

`10x^2+53x+63\text{ is a polynomial with degree 2.}`

The multiplication of the polynomial is polynomial,

It gives the closure property of the polynomials by multiplication.