Question

Find the difference of the polynomials given below and classify it in terms of degree and number of terms. 3n^2(n^2+4n-5)-(2n^2-n^4+3)

Answer 1

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

Here are the steps in finding the difference of the given polynomial.

1. Simplify the first term by multiplying 3n² by the terms inside the parenthesis.

`(3n^2)(n^2)+(3n^2)(4n)+(3n^2)(-5)-(2n^2-n^4+3)`
`3n^4+12n^3-15n^2-(2n^2-n^4+3)`

2. Eliminate the parenthesis on the second term by multiplying the negative symbol by the terms inside the parenthesis.

`3n^4+12n^3-15n^2-2n^2+n^4-3`

3. Arrange the terms according to their exponents or degree.

`3n^4+n^4+12n^3-15n^2-2n^2-3`

4. Combine similar terms. Similar terms are terms with the same variable and with the same exponent like 3n⁴ and n⁴.

`4n^4+12n^3-17n^2-3`

Hence, the difference between the given polynomial is 4n⁴ + 12n³ - 17n² - 3 as shown above.

The degree of the polynomial is 4.

There are 4 terms in the polynomial.