Factor Trinomials Practice Worksheet
TEKS AR.4D • Factoring Practice
Factor out Greatest Common Factor (GCF) and factor quadratic trinomials
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Date:
Period:
AR.4D Question 11 Practice (Factor GCF & Trinomial)
11A. Write as a product of factors:
\(g(x) = 3x^3 - 14x^2 + 8x\)
g(x) = ___ ( _______ ) ( _______ )
11B. Write as a product of factors:
\(g(x) = 2x^3 - 11x^2 + 12x\)
g(x) = ___ ( _______ ) ( _______ )
AR.4D Question 12 Practice (Leading Coefficient 5)
12A. Write as a product of factors:
\(g(x) = 5x^3 - 17x^2 + 6x\)
g(x) = ___ ( _______ ) ( _______ )
12B. Write as a product of factors:
\(g(x) = 5x^3 - 23x^2 + 12x\)
g(x) = ___ ( _______ ) ( _______ )
TEKS AR.4D • Factoring Practice (Cont.)
Factor out Greatest Common Factor (GCF) and factor quadratic trinomials
Name:
Page: 2 of 2
AR.4D Question 13 Practice (Leading Coefficient 6)
13A. Write as a product of factors:
\(g(x) = 6x^3 - 25x^2 + 4x\)
g(x) = ___ ( _______ ) ( _______ )
13B. Write as a product of factors:
\(g(x) = 6x^3 - 17x^2 + 12x\)
g(x) = ___ ( _______ ) ( _______ )
AR.4D Question 14 Practice (Leading Coefficient 7)
14A. Write as a product of factors:
\(g(x) = 7x^3 - 23x^2 + 6x\)
g(x) = ___ ( _______ ) ( _______ )
14B. Write as a product of factors:
\(g(x) = 7x^3 - 18x^2 + 8x\)
g(x) = ___ ( _______ ) ( _______ )
Factor Trinomials Answer Key
TEKS AR.4D • Factoring Practice
Answer Key
Complete step-by-step worked solutions and final factored forms
Standard: AR.4D
Page: 1 of 2
AR.4D Question 11 Practice (Factor GCF & Trinomial)
11A. Write as a product of factors:
\(g(x) = 3x^3 - 14x^2 + 8x\)
Step 1: Factor out GCF \(x\)
\(g(x) = x(3x^2 - 14x + 8)\)
Step 2: AC Method (\(ac = 24, b = -14\))
Find factors of \(24\) that add to \(-14\): \(-12\) and \(-2\)
Step 3: Factor by Grouping
\(3x^2 - 12x - 2x + 8 = 3x(x - 4) - 2(x - 4) = (3x - 2)(x - 4)\)
g(x) = x ( 3x - 2 )( x - 4 )
11B. Write as a product of factors:
\(g(x) = 2x^3 - 11x^2 + 12x\)
Step 1: Factor out GCF \(x\)
\(g(x) = x(2x^2 - 11x + 12)\)
Step 2: AC Method (\(ac = 24, b = -11\))
Find factors of \(24\) that add to \(-11\): \(-8\) and \(-3\)
Step 3: Factor by Grouping
\(2x^2 - 8x - 3x + 12 = 2x(x - 4) - 3(x - 4) = (2x - 3)(x - 4)\)
g(x) = x ( 2x - 3 )( x - 4 )
AR.4D Question 12 Practice (Leading Coefficient 5)
12A. Write as a product of factors:
\(g(x) = 5x^3 - 17x^2 + 6x\)
Step 1: Factor out GCF \(x\)
\(g(x) = x(5x^2 - 17x + 6)\)
Step 2: AC Method (\(ac = 30, b = -17\))
Find factors of \(30\) that add to \(-17\): \(-15\) and \(-2\)
Step 3: Factor by Grouping
\(5x^2 - 15x - 2x + 6 = 5x(x - 3) - 2(x - 3) = (5x - 2)(x - 3)\)
g(x) = x ( 5x - 2 )( x - 3 )
12B. Write as a product of factors:
\(g(x) = 5x^3 - 23x^2 + 12x\)
Step 1: Factor out GCF \(x\)
\(g(x) = x(5x^2 - 23x + 12)\)
Step 2: AC Method (\(ac = 60, b = -23\))
Find factors of \(60\) that add to \(-23\): \(-20\) and \(-3\)
Step 3: Factor by Grouping
\(5x^2 - 20x - 3x + 12 = 5x(x - 4) - 3(x - 4) = (5x - 3)(x - 4)\)
g(x) = x ( 5x - 3 )( x - 4 )
TEKS AR.4D • Factoring Practice (Cont.)
Answer Key
Complete step-by-step worked solutions and final factored forms
Standard: AR.4D
Page: 2 of 2
AR.4D Question 13 Practice (Leading Coefficient 6)
13A. Write as a product of factors:
\(g(x) = 6x^3 - 25x^2 + 4x\)
Step 1: Factor out GCF \(x\)
\(g(x) = x(6x^2 - 25x + 4)\)
Step 2: AC Method (\(ac = 24, b = -25\))
Find factors of \(24\) that add to \(-25\): \(-24\) and \(-1\)
Step 3: Factor by Grouping
\(6x^2 - 24x - x + 4 = 6x(x - 4) - 1(x - 4) = (6x - 1)(x - 4)\)
g(x) = x ( 6x - 1 )( x - 4 )
13B. Write as a product of factors:
\(g(x) = 6x^3 - 17x^2 + 12x\)
Step 1: Factor out GCF \(x\)
\(g(x) = x(6x^2 - 17x + 12)\)
Step 2: AC Method (\(ac = 72, b = -17\))
Find factors of \(72\) that add to \(-17\): \(-9\) and \(-8\)
Step 3: Factor by Grouping
\(6x^2 - 9x - 8x + 12 = 3x(2x - 3) - 4(2x - 3) = (2x - 3)(3x - 4)\)
g(x) = x ( 2x - 3 )( 3x - 4 )
AR.4D Question 14 Practice (Leading Coefficient 7)
14A. Write as a product of factors:
\(g(x) = 7x^3 - 23x^2 + 6x\)
Step 1: Factor out GCF \(x\)
\(g(x) = x(7x^2 - 23x + 6)\)
Step 2: AC Method (\(ac = 42, b = -23\))
Find factors of \(42\) that add to \(-23\): \(-21\) and \(-2\)
Step 3: Factor by Grouping
\(7x^2 - 21x - 2x + 6 = 7x(x - 3) - 2(x - 3) = (7x - 2)(x - 3)\)
g(x) = x ( 7x - 2 )( x - 3 )
14B. Write as a product of factors:
\(g(x) = 7x^3 - 18x^2 + 8x\)
Step 1: Factor out GCF \(x\)
\(g(x) = x(7x^2 - 18x + 8)\)
Step 2: AC Method (\(ac = 56, b = -18\))
Find factors of \(56\) that add to \(-18\): \(-14\) and \(-4\)
Step 3: Factor by Grouping
\(7x^2 - 14x - 4x + 8 = 7x(x - 2) - 4(x - 2) = (7x - 4)(x - 2)\)
g(x) = x ( 7x - 4 )( x - 2 )
