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Q5.

Expert-verifiedFound in: Page 466

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.

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

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.

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