Use Synthetic Division to Find the Quotient and the Remainder $\frac { 4 x ^ { 4 } + 16 x ^ { 3 } + 24 x ^ { 2 } + 16 x + 4 } { x + 1 }$

question 19

Multiple Choice

Use synthetic division to find the quotient and the remainder. $\frac { 4 x ^ { 4 } + 16 x ^ { 3 } + 24 x ^ { 2 } + 16 x + 4 } { x + 1 }$

• A) \(\text { quotient: } 4 x ^ { 3 } + 20 x ^ { 2 } + 12 x + 4 \text {; remainder: } 0\)
• B) \(\text { quotient: } 4 x ^ { 3 } + 12 x ^ { 2 } + 12 x + 4 \text {; remainder: } 0\)
• C) \(\text { quotient: } 4 x ^ { 3 } + 4 x ^ { 2 } + 12 x - 12 \text {; remainder: } 3\)
• D) \(\text { quotient: } 4 x ^ { 3 } + 12 x ^ { 2 } + 12 x + 4 \text {; remainder: } 3\)
• E) \(\text { quotient: } 4 x ^ { 3 } - 12 x ^ { 2 } + 4 x + 12 \text {; remainder: } 0\)

---

Definitions:

Stable Trait

A characteristic of an individual that is relatively enduring and consistent across different situations and over time.

Adverse Situations

Unfavorable, difficult, or challenging circumstances that an individual may face, which can impact their well-being and responses.

Affection

A feeling of fondness or love towards someone or something, often displayed through physical closeness or emotional gestures.

Routine

A set of habitual or fixed actions performed regularly, often contributing to discipline or efficiency in daily activities.