Question

Read each question. Then fill in the correct answer on the answer document provided by your teacher or on a sheet of paper.

Subtract the polynomials below.

$\left(7a^2+6a-2\right)-\left(-4a^3+3a^2+5\right)$

1. $4a^3+4a^2+6a-7$
2. $11a^2+3a-7$
3. $4a^3+10a^2+6a+3$
4. $4a^3+7a^3-3a$

Short answer

The result obtained after the subtraction of the given polynomials is $4a^3+4a^2+6a-7$. Therefore, the option A is correct.

Step-by-step solution

Step 1. Define the additive inverse.

The additive inverse of a number ‘$a$’ is$-a$ as $a+\left(-a\right)=0$.

Step 2. Find the result obtained after the subtraction of the given polynomials.

The difference of the polynomials $7a^2+6a-2$and $-4a^3+3a^2+5$can be find out by adding the polynomial $7a^2+6a-2$and additive inverse of the polynomial $-4a^3+3a^2+5$.

The additive inverse of the polynomial$-4a^3+3a^2+5$ is:

role="math" localid="1647689278588" $4a^3-3a^2-5$

Therefore, it can be noticed that:

role="math" localid="1647689455168" $$\begin{gathered} \left(7a^2+6a-2\right)-\left(-4a^3+3a^2+5\right)=\left(7a^2+6a-2\right)+\left(4a^3-3a^2-5\right) \\ =7a^2+6a-2+4a^3-3a^2-5 \\ =4a^3+7a^2-3a^2+6a-2-5 \\ =4a^3+4a^2+6a-7 \end{gathered}$$

Therefore, the result obtained after the subtraction of the given polynomials is $4a^3+4a^2+6a-7$. Therefore, the option A is correct.