Polynomial Operations Practice

Practice Worksheet

Name: _________________________

Date: __________________________

Lesson 1: Adding & Subtracting Polynomials

1. \((5x^2 + 3x - 1) + (2x^2 - x + 4)\)

\(7x^2 + 2x + 3\)

2. \((9y^3 - 2y) - (y^3 + 5y - 7)\)

\(8y^3 - 7y + 7\)

3. \((a^2 - 10) + (4a^2 + 3a)\)

\(5a^2 + 3a - 10\)

4. \((7k+4) - (8k+1)\)

\(-k + 3\)

5. \((6m^3 + 2m) + (m^3 - 7m + 1)\)

\(7m^3 - 5m + 1\)

6. \((3x^2 - 4x) - (5x^2 - 2x)\)

\(-2x^2 - 2x\)

7. \((12n^2 + n - 8) - (4n^2 - 3n - 5)\)

\(8n^2 + 4n - 3\)

8. Add: \((x^3 + x^2)\) and \((2x^3 - 4x^2)\)

\(3x^3 - 3x^2\)

Lesson 2: Multiplying Polynomials

1. \((x + 7)(x + 5)\)

\(x^2 + 12x + 35\)

2. \((n - 4)(n - 2)\)

\(n^2 - 6n + 8\)

3. \((3y + 1)(y - 6)\)

\(3y^2 - 17y - 6\)

4. \((x + 3)(x^2 + 2x - 5)\)

\(x^3 + 5x^2 + x - 15\)

5. \((2k - 5)(k + 4)\)

\(2k^2 + 3k - 20\)

6. \((x - 1)(x + 1)\)

\(x^2 - 1\)

7. \((4p + 3)^2\)

\(16p^2 + 24p + 9\)

8. \((m - 2)(m^2 - 4m + 3)\)

\(m^3 - 6m^2 + 11m - 6\)

Lesson 3: Factoring (GCF)

1. \(9x + 21\)

\(3(3x + 7)\)

2. \(10y^2 - 15y\)

\(5y(2y - 3)\)

3. \(8a^3 + 4a^2\)

\(4a^2(2a + 1)\)

4. \(6k^3 - 18k^2 + 12k\)

\(6k(k^2 - 3k + 2)\)

5. \(18m^2 - 6m\)

\(6m(3m - 1)\)

6. \(7x^3 + 21x^2\)

\(7x^2(x + 3)\)

7. \(50p^5 - 20p^3\)

\(10p^3(5p^2 - 2)\)

8. \(x^4y + x^3y^2\)

\(x^3y(x + y)\)

Lesson 4: Factoring Trinomials (a=1)

1. \(x^2 + 10x + 21\)

\((x+7)(x+3)\)

2. \(y^2 - 11y + 24\)

\((y-8)(y-3)\)

3. \(n^2 + 4n - 32\)

\((n+8)(n-4)\)

4. \(k^2 - 5k - 36\)

\((k-9)(k+4)\)

5. \(a^2 + 12a + 27\)

\((a+3)(a+9)\)

6. \(b^2 - 6b + 9\)

\((b-3)^2\)

7. \(c^2 + c - 20\)

\((c+5)(c-4)\)

8. \(d^2 - 3d - 40\)

\((d-8)(d+5)\)

Lesson 5: Factoring Trinomials (a>1)

1. \(2x^2 + 13x + 15\)

\((2x+3)(x+5)\)

2. \(3y^2 - 17y + 10\)

\((3y-2)(y-5)\)

3. \(5n^2 + 7n - 6\)

\((5n-3)(n+2)\)

4. \(4k^2 - 15k - 4\)

\((4k+1)(k-4)\)

5. \(7x^2 + 22x + 3\)

\((7x+1)(x+3)\)

6. \(6y^2 - 19y + 15\)

\((2y-3)(3y-5)\)

7. \(2n^2 + 5n - 12\)

\((2n-3)(n+4)\)

8. \(8k^2 - 10k - 3\)

\((4k+1)(2k-3)\)

Lesson 6: Dividing Polynomials

1. \(\frac{18x^4 + 27x^2}{9x}\)

\(2x^3 + 3x\)

2. \((x^2 + 8x + 15) \div (x+3)\)

\(x+5\)

3. \(\frac{20a^5 - 5a^3 + 10a^2}{5a^2}\)

\(4a^3 - a + 2\)

4. \((k^2 - 9k + 14) \div (k-7)\)

\(k-2\)

5. \(\frac{14y^5 - 35y^3}{7y^2}\)

\(2y^3 - 5y\)

6. \((x^2 - 4x - 45) \div (x-9)\)

\(x+5\)

7. \(\frac{8m^3+16m^2-24m}{8m}\)

\(m^2 + 2m - 3\)

8. \((2n^2 + 13n + 15) \div (n+5)\)

\(2n+3\)