Factored Form:
14
\(3m^3 - 2m^2 - 27m + 18\)
Show Work / Intermediate Steps:
Factored Form:
15
\(7x^3 - 2x^2 + 28x - 8\)
Show Work / Intermediate Steps:
Factored Form:
Factor Mastery Worksheet • Grade 11 Algebra II Page 3 of 7
Factor Mastery | Name: Date:
Part 4 Score: / 5
Factor into binomial products: \(x^2 + bx + c\)
16
\(x^2 - 14x + 45\)
Show Work / Intermediate Steps:
Factored Form:
17
\(x^2 + 4xy - 21y^2\)
Show Work / Intermediate Steps:
Factored Form:
18
\(x^2 - 7x - 60\)
Show Work / Intermediate Steps:
Factored Form:
19
\(x^4 - 3x^2 - 40\)
Show Work / Intermediate Steps:
Factored Form:
20
\(a^2 + 17ab + 72b^2\)
Show Work / Intermediate Steps:
Factored Form:
Factor Mastery Worksheet • Grade 11 Algebra II Page 4 of 7
Factor Mastery | Name: Date:
Part 5 Score: / 5
Factor completely using decomposition or grouping: \(ax^2 + bx + c\)
21
\(5x^2 + 17x + 6\)
Show Work / Intermediate Steps:
Factored Form:
22
\(4x^2 - 7x - 15\)
Show Work / Intermediate Steps:
Factored Form:
23
\(2x^2 + 9x + 4\)
Show Work / Intermediate Steps:
Factored Form:
24
\(3x^2 - 8x + 4\)
Show Work / Intermediate Steps:
Factored Form:
25
\(2x^2 + 3x - 5\)
Show Work / Intermediate Steps:
Factored Form:
Factor Mastery Worksheet • Grade 11 Algebra II Page 5 of 7
Factor Mastery | Name: Date:
Part 6 Score: / 5
Factor as a binomial squared: \(A^2 \pm 2AB + B^2 = (A \pm B)^2\)
26
\(x^2 - 18x + 81\)
Show Work / Intermediate Steps:
Factored Form:
27
\(16x^2 + 56x + 49\)
Show Work / Intermediate Steps:
Factored Form:
28
\(36x^2 - 60xy + 25y^2\)
Show Work / Intermediate Steps:
Factored Form:
29
\(25x^4 + 70x^2 + 49\)
Show Work / Intermediate Steps:
Factored Form:
30
\(64a^2 - 48ab + 9b^2\)
Show Work / Intermediate Steps:
Factored Form:
Factor Mastery Worksheet • Grade 11 Algebra II Page 6 of 7
Answer Key • Solutions Algebra II • Grade 11
30 Comprehensive Problems
Fully factored over the integers
Part 1: Greatest Common Factor (GCF) Problems 1–5
1
\(24x^5y^2 - 16x^3y^4 + 32x^2y^3\) → \(8x^2y^2(3x^3 - 2xy^2 + 4y)\)
2
\(-21a^4b^3c^2 + 35a^3b^2c^4 - 14a^2b^5c^2\) → \(-7a^2b^2c^2(3a^2b - 5c^2 + 2b^3)\)
3
\(36m^5n^2 + 54m^3n^4 - 90m^2n^3\) → \(18m^2n^2(2m^3 + 3mn^2 - 5n)\)
4
\(45p^5q^4 - 60p^4q^6 + 75p^3q^3\) → \(15p^3q^3(3p^2q - 4pq^3 + 5)\)
5
\(12x^2(2x - 5) - 8x(2x - 5)\) → \(4x(2x - 5)(3x - 2)\)
Part 2: Difference of Squares Problems 6–10
6
\((8x - 9y)(8x + 9y)\)
7
\((9x^2+4)(9x^2-4) \rightarrow\) \((9x^2 + 4)(3x - 2)(3x + 2)\)
8
\(5x(x^2 - 16) \rightarrow\) \(5x(x - 4)(x + 4)\)
9
\((6a^3 - 7b^2)(6a^3 + 7b^2)\)
10
\(3x(x^4 - 81) \rightarrow\) \(3x(x^2 + 9)(x - 3)(x + 3)\)
Part 3: Factoring by Grouping Problems 11–15
11
\((x+5)(x^2-4) \rightarrow\) \((x + 5)(x - 2)(x + 2)\)
12
\(2x^2(5x-3)+5(5x-3) \rightarrow\) \((5x - 3)(2x^2 + 5)\)
13
\((3x - 2y)(5a + 7b)\)
14
\((3m-2)(m^2-9) \rightarrow\) \((3m - 2)(m - 3)(m + 3)\)
15
\(x^2(7x-2)+4(7x-2) \rightarrow\) \((7x - 2)(x^2 + 4)\)
Part 4: Trinomials (\(a = 1\)) Problems 16–20
16
\((x - 5)(x - 9)\)
17
\((x + 7y)(x - 3y)\)
18
\((x - 12)(x + 5)\)
19
Let \(u = x^2 \rightarrow\) \((x^2 - 8)(x^2 + 5)\)
20
\((a + 8b)(a + 9b)\)
Part 5: Trinomials (\(a > 1\)) Problems 21–25
21
\(5x(x+3)+2(x+3) \rightarrow\) \((5x + 2)(x + 3)\)
22
\(4x(x-3)+5(x-3) \rightarrow\) \((4x + 5)(x - 3)\)
23
\(2x(x+4)+1(x+4) \rightarrow\) \((2x + 1)(x + 4)\)
24
\(3x(x-2)-2(x-2) \rightarrow\) \((3x - 2)(x - 2)\)
25
\(2x(x-1)+5(x-1) \rightarrow\) \((2x + 5)(x - 1)\)
Part 6: Perfect Square Trinomials Problems 26–30
26
\((x - 9)^2\)
27
\((4x + 7)^2\)
28
\((6x - 5y)^2\)
29
\((5x^2 + 7)^2\)
30
\((8a - 3b)^2\)
Factor Mastery Worksheet • Grade 11 Algebra II Page 7 of 7 • Answer Key
