Question

What polynomial must be added to x²-2x+6 so that the sum is x³+7x ? Show Your Work.

Answer 1

To find the polynomial that must be added to x²-2x+6 to get x³+7x, subtract the given polynomial from the desired polynomial. The resulting polynomial is x³-x²+9x-6.

Step-by-step explanation:

To find the polynomial that must be added to x²-2x+6 to get x³+7x, we can subtract the given polynomial from the desired polynomial. In this case, we get:

(x³+7x) - (x²-2x+6)

Simplifying, we combine like terms and rearrange the terms in descending order of exponents:

x³+7x-x²+2x-6

The resulting polynomial is x³-x²+9x-6. Therefore, x³-x²+9x-6 must be added to x²-2x+6 to have the sum of x³+7x.