Question

What should be added to $6a^3+5a-2a^2-7$ to get $9a^2-2a-a^3+2$?

• A. $5a^3+7a^2-3a+5$
• B. $7a^3-11a^2+7a-9$
• C. $-7a^3+11a^2-7a+9$
• D. $5a^3+9a^2-5a+3$

Answer 1

The correct option is C $-7a^3+11a^2-7a+9$

Let 'y' be the term to be added to $6a^3+5a-2a^2-7$ to get $9a^2-2a-a^3+2$
= $6a^3+5a-2a^2-7+y=9a^2-2a-a^3+2$
Subtracting $6a^3+5a-2a^2-7$ from $9a^2-2a-a^3+2$,
= $(-a^3+9a^2-2a+2)$ - $(6a^3-2a^2+5a-7)$
= $(-a^3-6a^3)+(9a^2+2a^2)+(-2a-5a)+(2+7)$,
= $-7a^3+11a^2-7a+9$