Question

Write the sum of 5x^2+2x-10 and 2x^3+6 as a polynomial in standard form

Answer 1

Given polynomials:

`\begin{gathered} 5x^2\text{ + 2x - 10} \\ 2x^2\text{ + 6 } \end{gathered}`

The sum of the polynomials is:

`=\text{ 5x}^2\text{ + 2x - 10 + \lparen2x}^2\text{ + 6\rparen}`

Simplifying the sum:

`\begin{gathered} =\text{ 5x}^2\text{ + 2x - 10 + 2x}^2\text{ + 6} \\ Collect\text{ like terms} \\ \text{ = 5x}^2\text{ + 2x}^2\text{ + 2x - 10 + 6} \\ =\text{ 7x}^2\text{ + 2x - 4} \end{gathered}`

Hence,the sum of the polynomials in standard form is:

`=\text{ 7x}^2\text{ + 2x - 4}`