Combine like terms to simplify the expression $z ^ { 3 } + 4 z ^ { 2 } + z + z ^ { 2 } + 6 z + 1$.
A) $14 z ^ { 9 }$
B) $z ^ { 3 } + 13 z ^ { 2 }$
C) $z ^ { 3 } + 5 z ^ { 2 } + 7 z + 1$
D) $13 z ^ { 9 } + 1$
E) $z ^ { 3 } + 12 z ^ { 2 } + 1$

Question

Quizplus · Accepted Answer

To simplify the expression, we can combine like terms by adding the coefficients of the terms with the same variable exponent.

Starting with the highest degree term, we have: 
$$z^3 + \underbrace{4z^2}_\text{first} + z + \underbrace{z^2}_\text{second} + \underbrace{6z}_\text{third} + 1$$

Combining like terms, we have: 
$$z^3 + (4z^2 + z^2) + (z + 6z) + 1 = z^3 + 5z^2 + 7z + 1$$

Therefore, the simplified expression is $z ^ { 3 } + 5 z ^ { 2 } + 7 z + 1$, which is answer choice C.

Combine Like Terms to Simplify the Expression z3+4z2+z+z2+6z+1z ^ { 3 } + 4 z ^ { 2 } + z + z ^ { 2 } + 6 z + 1z3+4z2+z+z2+6z+1

Combine Like Terms to Simplify the Expression $z ^ { 3 } + 4 z ^ { 2 } + z + z ^ { 2 } + 6 z + 1$