Question

What polynomial must be added to x² - 2x + 6 so that the sum is 3x^2 + 7x ? A. 4x^2 + 5x + 6 B. 3x² + 9x + 6 C. 3x² + 9x - 6 D. 2x² + 9x - 6 E. 2x^2 – 5x + 6

Answer 1

The polynomial that must be added is;

`2x^2+9x-6`

Step-by-step explanation:

Given the polynomial;

`x^2-2x+6`

We want to find the polynomial that must be added to it to give the polynomial;

`3x^2+7x`

To get that we will subtract the polynomial from the sum;

`\begin{gathered} 3x^2+7x-(x^2-2x+6) \\ =3x^2+7x-x^2+2x-6) \\ \text{rearranging;} \\ =3x^2-x^2+7x+2x-6 \\ \text{simplifying;} \\ =2x^2+9x-6 \end{gathered}`

Therefore, the polynomial that must be added is;

`2x^2+9x-6`