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Expert-verified Found in: Page 466 ### Algebra 1

Book edition Student Edition
Author(s) Carter, Cuevas, Day, Holiday, Luchin
Pages 801 pages
ISBN 9780078884801 # 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(7{a}^{2}+6a-2\right)-\left(-4{a}^{3}+3{a}^{2}+5\right)$$4{a}^{3}+4{a}^{2}+6a-7$$11{a}^{2}+3a-7$$4{a}^{3}+10{a}^{2}+6a+3$$4{a}^{3}+7{a}^{3}-3a$

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

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

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

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

Therefore, it can be noticed that:

role="math" localid="1647689455168" $\left(7{a}^{2}+6a-2\right)-\left(-4{a}^{3}+3{a}^{2}+5\right)=\left(7{a}^{2}+6a-2\right)+\left(4{a}^{3}-3{a}^{2}-5\right)\phantom{\rule{0ex}{0ex}}=7{a}^{2}+6a-2+4{a}^{3}-3{a}^{2}-5\phantom{\rule{0ex}{0ex}}=4{a}^{3}+7{a}^{2}-3{a}^{2}+6a-2-5\phantom{\rule{0ex}{0ex}}=4{a}^{3}+4{a}^{2}+6a-7$

Therefore, the result obtained after the subtraction of the given polynomials is $4{a}^{3}+4{a}^{2}+6a-7$. Therefore, the option A is correct. ### Want to see more solutions like these? 