Question

Combine like terms to simplify the following polynomial: 2x + 3z - x + 5z.

A) 11xz
B) 3x - 7z
C) x + 8z
D) 2x² + 3z²

Answer 1

Combining like terms of the polynomial 2x + 3z - x + 5z results in x + 8z, which corresponds to answer option C). Like terms are combined by adding or subtracting the coefficients, ensuring the final answer is checked for reasonableness.

Step-by-step explanation:

To combine like terms and simplify the polynomial 2x + 3z - x + 5z, we look for terms that have the same variable raised to the same power. In this case, 2x and -x are like terms as well as 3z and 5z.

Combining the x terms:

• 2x - x = x

And combining the z terms:

• 3z + 5z = 8z

Putting it all together, we get:

x + 8z

Therefore, the simplified polynomial is x + 8z, which corresponds to option C).

Finally, we check if the answer is reasonable by verifying that the combined terms make sense arithmetically.