Solved Date Name Per Algebra 1- 10.1 Worksheet - Adding and ... - Free Printable

To solve the problems involving adding and subtracting polynomials, we need to combine like terms. Let's go through each problem step by step.

Section 1: Adding Polynomials

#### Problem 1:
\[
(5x^2 - 8x + 1) + (2x^2 - 4x - 11)
\]

1. Combine the coefficients of \(x^2\):
\[
5x^2 + 2x^2 = 7x^2
\]

2. Combine the coefficients of \(x\):
\[
-8x - 4x = -12x
\]

3. Combine the constant terms:
\[
1 - 11 = -10
\]

4. Write the final polynomial:
\[
7x^2 - 12x - 10
\]

Answer:
\[
\boxed{7x^2 - 12x - 10}
\]

#### Problem 2:
\[
(3x^2 - 4x - 1) + (8x^2 - x + 6)
\]

1. Combine the coefficients of \(x^2\):
\[
3x^2 + 8x^2 = 11x^2
\]

2. Combine the coefficients of \(x\):
\[
-4x - x = -5x
\]

3. Combine the constant terms:
\[
-1 + 6 = 5
\]

4. Write the final polynomial:
\[
11x^2 - 5x + 5
\]

Answer:
\[
\boxed{11x^2 - 5x + 5}
\]

#### Problem 3:
\[
(14x^2 - 11x - 2) + (3x^2 + 6x - 5)
\]

1. Combine the coefficients of \(x^2\):
\[
14x^2 + 3x^2 = 17x^2
\]

2. Combine the coefficients of \(x\):
\[
-11x + 6x = -5x
\]

3. Combine the constant terms:
\[
-2 - 5 = -7
\]

4. Write the final polynomial:
\[
17x^2 - 5x - 7
\]

Answer:
\[
\boxed{17x^2 - 5x - 7}
\]

#### Problem 4:
\[
(6x^2 - x - 4) + (2x^2 + 5x - 5)
\]

1. Combine the coefficients of \(x^2\):
\[
6x^2 + 2x^2 = 8x^2
\]

2. Combine the coefficients of \(x\):
\[
-x + 5x = 4x
\]

3. Combine the constant terms:
\[
-4 - 5 = -9
\]

4. Write the final polynomial:
\[
8x^2 + 4x - 9
\]

Answer:
\[
\boxed{8x^2 + 4x - 9}
\]

#### Problem 5:
\[
(5x^2 + 2x - 1) + (4x^2 - x - 9)
\]

1. Combine the coefficients of \(x^2\):
\[
5x^2 + 4x^2 = 9x^2
\]

2. Combine the coefficients of \(x\):
\[
2x - x = x
\]

3. Combine the constant terms:
\[
-1 - 9 = -10
\]

4. Write the final polynomial:
\[
9x^2 + x - 10
\]

Answer:
\[
\boxed{9x^2 + x - 10}
\]

#### Problem 6:
\[
(4x^2 + 2x - 5) + (6x^2 - x - 5)
\]

1. Combine the coefficients of \(x^2\):
\[
4x^2 + 6x^2 = 10x^2
\]

2. Combine the coefficients of \(x\):
\[
2x - x = x
\]

3. Combine the constant terms:
\[
-5 - 5 = -10
\]

4. Write the final polynomial:
\[
10x^2 + x - 10
\]

Answer:
\[
\boxed{10x^2 + x - 10}
\]

Section 2: Subtracting Polynomials

#### Problem 7:
\[
(3x^2 - x + 4) - (x^2 - 5x - 5)
\]

1. Distribute the negative sign to the second polynomial:
\[
3x^2 - x + 4 - x^2 + 5x + 5
\]

2. Combine the coefficients of \(x^2\):
\[
3x^2 - x^2 = 2x^2
\]

3. Combine the coefficients of \(x\):
\[
-x + 5x = 4x
\]

4. Combine the constant terms:
\[
4 + 5 = 9
\]

5. Write the final polynomial:
\[
2x^2 + 4x + 9
\]

Answer:
\[
\boxed{2x^2 + 4x + 9}
\]

#### Problem 8:
\[
(4x^2 - x - 7) - (2x^3 + 6x^2 - 11)
\]

1. Distribute the negative sign to the second polynomial:
\[
4x^2 - x - 7 - 2x^3 - 6x^2 + 11
\]

2. Combine the coefficients of \(x^3\):
\[
-2x^3
\]

3. Combine the coefficients of \(x^2\):
\[
4x^2 - 6x^2 = -2x^2
\]

4. Combine the coefficients of \(x\):
\[
-x
\]

5. Combine the constant terms:
\[
-7 + 11 = 4
\]

6. Write the final polynomial:
\[
-2x^3 - 2x^2 - x + 4
\]

Answer:
\[
\boxed{-2x^3 - 2x^2 - x + 4}
\]

#### Problem 9:
\[
(3x^3 + 2x^2 - 5x) - (4x^2 - 7x + 5)
\]

1. Distribute the negative sign to the second polynomial:
\[
3x^3 + 2x^2 - 5x - 4x^2 + 7x - 5
\]

2. Combine the coefficients of \(x^3\):
\[
3x^3
\]

3. Combine the coefficients of \(x^2\):
\[
2x^2 - 4x^2 = -2x^2
\]

4. Combine the coefficients of \(x\):
\[
-5x + 7x = 2x
\]

5. Combine the constant terms:
\[
-5
\]

6. Write the final polynomial:
\[
3x^3 - 2x^2 + 2x - 5
\]

Answer:
\[
\boxed{3x^3 - 2x^2 + 2x - 5}
\]

#### Problem 10:
\[
(2x^3 - x + 4) - (5x^2 - 6x - 5)
\]

1. Distribute the negative sign to the second polynomial:
\[
2x^3 - x + 4 - 5x^2 + 6x + 5
\]

2. Combine the coefficients of \(x^3\):
\[
2x^3
\]

3. Combine the coefficients of \(x^2\):
\[
-5x^2
\]

4. Combine the coefficients of \(x\):
\[
-x + 6x = 5x
\]

5. Combine the constant terms:
\[
4 + 5 = 9
\]

6. Write the final polynomial:
\[
2x^3 - 5x^2 + 5x + 9
\]

Answer:
\[
\boxed{2x^3 - 5x^2 + 5x + 9}
\]

#### Problem 11:
\[
(5x^3 - 6x + 4) + (x^2 - 7x - 11)
\]

1. Combine the coefficients of \(x^3\):
\[
5x^3
\]

2. Combine the coefficients of \(x^2\):
\[
x^2
\]

3. Combine the coefficients of \(x\):
\[
-6x - 7x = -13x
\]

4. Combine the constant terms:
\[
4 - 11 = -7
\]

5. Write the final polynomial:
\[
5x^3 + x^2 - 13x - 7
\]

Answer:
\[
\boxed{5x^3 + x^2 - 13x - 7}
\]

Final Answers:

\[
\boxed{
\begin{aligned}
1. & \ 7x^2 - 12x - 10 \\
2. & \ 11x^2 - 5x + 5 \\
3. & \ 17x^2 - 5x - 7 \\
4. & \ 8x^2 + 4x - 9 \\
5. & \ 9x^2 + x - 10 \\
6. & \ 10x^2 + x - 10 \\
7. & \ 2x^2 + 4x + 9 \\
8. & \ -2x^3 - 2x^2 - x + 4 \\
9. & \ 3x^3 - 2x^2 + 2x - 5 \\
10. & \ 2x^3 - 5x^2 + 5x + 9 \\
11. & \ 5x^3 + x^2 - 13x - 7 \\
\end{aligned}
}
\]