Question

sem 1 final study guide
divide.

1. $(m^3 + 14m^2 + 49m + 36) \div (m + 9$

Explanation:

Step1: Use Polynomial Long Division

We divide the polynomial \( m^3 + 14m^2 + 49m + 36 \) by \( m + 9 \).

First, divide the leading term of the dividend \( m^3 \) by the leading term of the divisor \( m \), we get \( m^2 \). Multiply \( m + 9 \) by \( m^2 \): \( m^2(m + 9)=m^3 + 9m^2 \). Subtract this from the dividend:

\( (m^3 + 14m^2 + 49m + 36)-(m^3 + 9m^2)=5m^2 + 49m + 36 \)

Step2: Continue the Division

Now, divide the leading term of the new dividend \( 5m^2 \) by \( m \), we get \( 5m \). Multiply \( m + 9 \) by \( 5m \): \( 5m(m + 9)=5m^2 + 45m \). Subtract this from the new dividend:

\( (5m^2 + 49m + 36)-(5m^2 + 45m)=4m + 36 \)

Step3: Final Division Step

Divide the leading term of the new dividend \( 4m \) by \( m \), we get \( 4 \). Multiply \( m + 9 \) by \( 4 \): \( 4(m + 9)=4m + 36 \). Subtract this from the new dividend:

\( (4m + 36)-(4m + 36)=0 \)

So the result of the division is \( m^2 + 5m + 4 \).

Answer:

\( m^2 + 5m + 4 \)