Question

Simplify the given poly nominal expressions and determined agree and number of terms in each expression

Answer 1

1. The given polynomial is:

`4x+2x^2(3x-5)`

Start by applying the distributive property:

`\begin{gathered} =4x+2x^2\cdot3x-2x^2\cdot5 \\ =4x+6x^3-10x^2 \end{gathered}`

Now, rearrange the terms so that they're written in descending order of exponent:

`6x^3-10x^2+4x`

The degree of a polynomial is given by the largest exponent, then its degree is 3 and the number of terms is 3.

2. Polynomial:

`(-3x^4+5x^3-12)+(7x^3-x^5+6)`

Start by combining like terms:

`\begin{gathered} =-3x^4+(5x^3+7x^3)-x^5-12+6 \\ =-3x^4+12x^3-x^5-6 \end{gathered}`

And rearrange the terms in descending order of exponent:

`-x^5-3x^4+12x^3-6`

The degree is 5 and the number of terms is 4.

3. Polynomial:

`(3x^2-3)(3x^2+3)`

It is the factored form of the difference of two squares:

`(a-b)(a+b)=a^2-b^2`

By replacing the known values we have:

`\begin{gathered} (3x^2-3)(3x^2+3)=(3x^2)^2-3^3 \\ =9x^4-9 \end{gathered}`

Then the degree is 4 and the number of terms is 2.