Question

1. $r^2 - 8r^3 - 7 + 8r^4 - 4r^3 + 4r^2$

a) $8r^4 - 9r^3 + 13r^2 + 1$
b) $8r^4 - 12r^3 + 13r^2 - 7$
c) $8r^4 - 12r^3 + 5r^2 - 7$
d) $8r^4 - 12r^3 + 13r^2 + 1$

Explanation:

Step1: Combine like terms for \( r^4 \)

The term with \( r^4 \) is \( 8r^4 \), so we keep it as is.

Step2: Combine like terms for \( r^3 \)

We have \( -8r^3 \) and \( -4r^3 \). Combining them: \( -8r^3 - 4r^3 = -12r^3 \)

Step3: Combine like terms for \( r^2 \)

We have \( r^2 \) and \( 4r^2 \). Combining them: \( r^2 + 4r^2 = 5r^2 \)

Step4: The constant term

The constant term is \( -7 \), so we keep it as is.

Putting it all together, the simplified polynomial is \( 8r^4 - 12r^3 + 5r^2 - 7 \)

Answer:

C) \( 8r^4 - 12r^3 + 5r^2 - 7 \)