Add the polynomial expressions 5z - 2z^2 - 4z + 5 and 6z^2 + 3 - 7z.

Question

9z^2 - 11z + 8
4z^2 - 6z + 8
4z^2 - z + 8
11z^2 + z - 2

Answer 1

To add the polynomial expressions $5z-2z^2-4z+5$ and $6z^2+3-7z$, we first rearrange and combine like terms.

1. Write the first polynomial: $$5z-2z^2-4z+5=-2z^2+(5z-4z)+5=-2z^2+1z+5$$

2. Write the second polynomial: $$6z^2+3-7z=6z^2+(-7z)+3$$

Now, we combine both polynomials: $$(-2z^2+z+5)+(6z^2-7z+3)$$

Now, add the like terms:

• Combine the $z^2$ terms: $-2z^2+6z^2=4z^2$
• Combine the $z$ terms: $z-7z=-6z$
• Combine the constant terms: $5+3=8$

Putting it all together: $$4z^2-6z+8$$

Thus, the sum of the two polynomial expressions is: $$\boxed{{\displaystyle 4z^2-6z+8}}$$