• Problem:
What polynomial can be added to x² - 2x + 6 so that the sum is 3x² + 7x?
• Solution:
To get the other added, you just need to subtract x² - 2x + 6 from 3x² + 7x.
- Expand the expression.
- Change the signs of the terms on the right side of the operation of subtraction.
- Simplify.
[tex] \large \boxed{\begin{array}{} \tt (3x²+7x ) -( x {}^{2} - 2x + 6 ) \\ \tt 3 {x}^{2} + 7x - x {}^{2} + 2x - 6 \\ \purple{ \tt 2x {}^{2} + 9x - 6} \end{array}}[/tex]
Try to check the answer by adding it from x² -2x + 6.
[tex] \large \boxed{\begin{array}{} \tt( x {}^{2} - 2x + 6 ) +(2x {}^{2} + 9x - 6) \\ \tt x {}^{2} - 2x + \cancel6 +2x {}^{2} + 9x - \cancel{ 6 }\\ \blue{\tt 3x {}^{2} + 7x }\end{array}}[/tex]
Thus, the answer is correct.
• Answer:
Polynomial 2x² + 9x - 6 can be added to x² - 2x + 6 so that the sum is 3x² + 7x.
