Question

add: $(g^2 - 4g^4 + 5g + 9) + (-3g^3 + 3g^2 - 6)$

1. rewrite terms that are subtracted as addition of the opposite.

$g^2 + (-4g^4) + 5g + 9 + (-3g^3) + 3g^2 + (-6)$

1. group like terms.
2. combine like terms.
3. write the resulting polynomial in standard form.

complete the steps to find the sum. what is the sum?
$\circ -7g^4 + 4g^3 - 3g^2 + 5g - 3$
$\circ -4g^4 - 3g^3 + 4g^2 + 5g + 3$
$\circ -4g^4 + 4g^2 + 14g - 6$
$\circ -3g^4 + 14g - 6$

Explanation:

Step1: Group like terms

$(-4g^4) + (-3g^3) + (g^2 + 3g^2) + 5g + (9 + (-6))$

Step2: Combine like terms

$-4g^4 - 3g^3 + 4g^2 + 5g + 3$

Step3: Verify standard form

Terms ordered by descending degree: $-4g^4 - 3g^3 + 4g^2 + 5g + 3$

Answer:

-4g⁴ - 3g³ + 4g² + 5g + 3 (matches option: $\boldsymbol{-4g^4 - 3g^3 + 4g^2 + 5g + 3}$)