Question

multiple choice, 1 point
find the difference of the following polynomials:
$(-2r^4 + 3r^3 - 10) - (4r^4 + r^3 + 2r^2 + 7)$
$2r^4+2r^3+2r^2 - 3$
$-6r^4+2r^3+2r^2 - 3$
$-6r^4+4r^3+2r^2 - 17$
$-6r^4+2r^3 - 2r^2 - 17$

Explanation:

Step1: Distribute the negative sign

$(-2r^4 + 3r^3 - 10) - 4r^4 - r^3 - 2r^2 - 7$

Step2: Combine like $r^4$ terms

$-2r^4 - 4r^4 = -6r^4$

Step3: Combine like $r^3$ terms

$3r^3 - r^3 = 2r^3$

Step4: Identify $r^2$ term

$-2r^2$ (no other $r^2$ terms to combine)

Step5: Combine constant terms

$-10 - 7 = -17$

Step6: Assemble the polynomial

$-6r^4 + 2r^3 - 2r^2 - 17$

Answer:

-6r⁴+2r³-2r²-17