Problem: Add the given polynomial equations.
We are tasked with adding the polynomials in each problem. To do this, we will combine like terms (terms with the same power of \( x \)).
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####
Problem 1:
\[
(16x^2 + 10x + 10) + (6x^2 + 6x + 11)
\]
1.
Combine the \( x^2 \)-terms:
\[
16x^2 + 6x^2 = 22x^2
\]
2.
Combine the \( x \)-terms:
\[
10x + 6x = 16x
\]
3.
Combine the constant terms:
\[
10 + 11 = 21
\]
4.
Write the final polynomial:
\[
22x^2 + 16x + 21
\]
Answer for Problem 1:
\[
\boxed{22x^2 + 16x + 21}
\]
---
####
Problem 2:
\[
(-19x^2 - 6x + 6) + (-8x^2 - 4x - 9) + (-12x^2 - 18x - 10)
\]
1.
Combine the \( x^2 \)-terms:
\[
-19x^2 - 8x^2 - 12x^2 = -39x^2
\]
2.
Combine the \( x \)-terms:
\[
-6x - 4x - 18x = -28x
\]
3.
Combine the constant terms:
\[
6 - 9 - 10 = -13
\]
4.
Write the final polynomial:
\[
-39x^2 - 28x - 13
\]
Answer for Problem 2:
\[
\boxed{-39x^2 - 28x - 13}
\]
---
####
Problem 3:
\[
(8x^2 - 9x + 12) + (-12x^2 - 9x - 19)
\]
1.
Combine the \( x^2 \)-terms:
\[
8x^2 - 12x^2 = -4x^2
\]
2.
Combine the \( x \)-terms:
\[
-9x - 9x = -18x
\]
3.
Combine the constant terms:
\[
12 - 19 = -7
\]
4.
Write the final polynomial:
\[
-4x^2 - 18x - 7
\]
Answer for Problem 3:
\[
\boxed{-4x^2 - 18x - 7}
\]
---
####
Problem 4:
\[
(-19x^2 - 15x - 12) + (11x^2 + 6x - 19)
\]
1.
Combine the \( x^2 \)-terms:
\[
-19x^2 + 11x^2 = -8x^2
\]
2.
Combine the \( x \)-terms:
\[
-15x + 6x = -9x
\]
3.
Combine the constant terms:
\[
-12 - 19 = -31
\]
4.
Write the final polynomial:
\[
-8x^2 - 9x - 31
\]
Answer for Problem 4:
\[
\boxed{-8x^2 - 9x - 31}
\]
---
####
Problem 5:
\[
(18x^2 + 3x + 16) + (13x^2 + 16x + 12)
\]
1.
Combine the \( x^2 \)-terms:
\[
18x^2 + 13x^2 = 31x^2
\]
2.
Combine the \( x \)-terms:
\[
3x + 16x = 19x
\]
3.
Combine the constant terms:
\[
16 + 12 = 28
\]
4.
Write the final polynomial:
\[
31x^2 + 19x + 28
\]
Answer for Problem 5:
\[
\boxed{31x^2 + 19x + 28}
\]
---
Final Answers:
1. \(\boxed{22x^2 + 16x + 21}\)
2. \(\boxed{-39x^2 - 28x - 13}\)
3. \(\boxed{-4x^2 - 18x - 7}\)
4. \(\boxed{-8x^2 - 9x - 31}\)
5. \(\boxed{31x^2 + 19x + 28}\)
Parent Tip: Review the logic above to help your child master the concept of polynomial equation worksheet.
