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Factoring ax² + bx + c Completely (GCF First) — Easy Worksheet 2
Grade 9 · Whoobee Name: ____________________ Date: __________
Factor completely. Take out the GCF first, then factor what is left, like 2(3x - 1)(x + 4).
How to solve
First take out the greatest common factor of all three terms. Then factor the trinomial left in the brackets: find two numbers that multiply to ac and add to b, split the middle term, and factor by grouping. Keep the GCF in front of the answer.
Example
Factor completely: 3x² + 18x + 24
Answer: 3(x + 2)(x + 4)
Not quite. The answer is
💡 The GCF of 2, 16 and 30 is 2, so 2x² + 16x + 30 = 2(x² + 8x + 15). Now factor x² + 8x + 15. Find two numbers that multiply to c = 15 and add to b = 8: 3 and 5, because 3 × 5 = 15 and 3 + 5 = 8. So x² + 8x + 15 = (x + 3)(x + 5). Keep the GCF in front: 2x² + 16x + 30 = 2(x + 3)(x + 5).
✓ Correct!
Not quite. The answer is
💡 The GCF of 2, 16 and 30 is 2, so 2x² + 16x + 30 = 2(x² + 8x + 15). Now factor x² + 8x + 15. Find two numbers that multiply to c = 15 and add to b = 8: 3 and 5, because 3 × 5 = 15 and 3 + 5 = 8. So x² + 8x + 15 = (x + 3)(x + 5). Keep the GCF in front: 2x² + 16x + 30 = 2(x + 3)(x + 5).
💡 How to solve: Factoring ax² + bx + c Completely (GCF First)
First take out the greatest common factor of all three terms. Then factor the trinomial left in the brackets: find two numbers that multiply to ac and add to b, split the middle term, and factor by grouping. Keep the GCF in front of the answer.
Try a similar one
Factor completely: 2x² - 6x - 8
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The GCF of 4, 4 and 48 is 4, so 4x² + 4x − 48 = 4(x² + x − 12). Now factor x² + x − 12. Find two numbers that multiply to c = −12 and add to b = 1: 4 and −3, because 4 × (−3) = −12 and 4 + (−3) = 1. So x² + x − 12 = (x + 4)(x − 3). Keep the GCF in front: 4x² + 4x − 48 = 4(x + 4)(x − 3).
✓ Correct!
Not quite. The answer is
💡 The GCF of 4, 4 and 48 is 4, so 4x² + 4x − 48 = 4(x² + x − 12). Now factor x² + x − 12. Find two numbers that multiply to c = −12 and add to b = 1: 4 and −3, because 4 × (−3) = −12 and 4 + (−3) = 1. So x² + x − 12 = (x + 4)(x − 3). Keep the GCF in front: 4x² + 4x − 48 = 4(x + 4)(x − 3).
💡 How to solve: Factoring ax² + bx + c Completely (GCF First)
First take out the greatest common factor of all three terms. Then factor the trinomial left in the brackets: find two numbers that multiply to ac and add to b, split the middle term, and factor by grouping. Keep the GCF in front of the answer.
Try a similar one
Factor completely: 4x² + 16x - 20
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The GCF of 4, 36 and 80 is 4, so 4x² − 36x + 80 = 4(x² − 9x + 20). Now factor x² − 9x + 20. Find two numbers that multiply to c = 20 and add to b = −9: −5 and −4, because −5 × (−4) = 20 and −5 + (−4) = −9. So x² − 9x + 20 = (x − 5)(x − 4). Keep the GCF in front: 4x² − 36x + 80 = 4(x − 5)(x − 4).
✓ Correct!
Not quite. The answer is
💡 The GCF of 4, 36 and 80 is 4, so 4x² − 36x + 80 = 4(x² − 9x + 20). Now factor x² − 9x + 20. Find two numbers that multiply to c = 20 and add to b = −9: −5 and −4, because −5 × (−4) = 20 and −5 + (−4) = −9. So x² − 9x + 20 = (x − 5)(x − 4). Keep the GCF in front: 4x² − 36x + 80 = 4(x − 5)(x − 4).
💡 How to solve: Factoring ax² + bx + c Completely (GCF First)
First take out the greatest common factor of all three terms. Then factor the trinomial left in the brackets: find two numbers that multiply to ac and add to b, split the middle term, and factor by grouping. Keep the GCF in front of the answer.
Try a similar one
Factor completely: 3x² + 3x - 36
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The GCF of 3, 12 and 9 is 3, so 3x² + 12x + 9 = 3(x² + 4x + 3). Now factor x² + 4x + 3. Find two numbers that multiply to c = 3 and add to b = 4: 3 and 1, because 3 × 1 = 3 and 3 + 1 = 4. So x² + 4x + 3 = (x + 3)(x + 1). Keep the GCF in front: 3x² + 12x + 9 = 3(x + 3)(x + 1).
✓ Correct!
Not quite. The answer is
💡 The GCF of 3, 12 and 9 is 3, so 3x² + 12x + 9 = 3(x² + 4x + 3). Now factor x² + 4x + 3. Find two numbers that multiply to c = 3 and add to b = 4: 3 and 1, because 3 × 1 = 3 and 3 + 1 = 4. So x² + 4x + 3 = (x + 3)(x + 1). Keep the GCF in front: 3x² + 12x + 9 = 3(x + 3)(x + 1).
💡 How to solve: Factoring ax² + bx + c Completely (GCF First)
First take out the greatest common factor of all three terms. Then factor the trinomial left in the brackets: find two numbers that multiply to ac and add to b, split the middle term, and factor by grouping. Keep the GCF in front of the answer.
Try a similar one
Factor completely: 4x² - 4x - 24
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The GCF of 4, 12 and 8 is 4, so 4x² − 12x + 8 = 4(x² − 3x + 2). Now factor x² − 3x + 2. Find two numbers that multiply to c = 2 and add to b = −3: −2 and −1, because −2 × (−1) = 2 and −2 + (−1) = −3. So x² − 3x + 2 = (x − 2)(x − 1). Keep the GCF in front: 4x² − 12x + 8 = 4(x − 2)(x − 1).
✓ Correct!
Not quite. The answer is
💡 The GCF of 4, 12 and 8 is 4, so 4x² − 12x + 8 = 4(x² − 3x + 2). Now factor x² − 3x + 2. Find two numbers that multiply to c = 2 and add to b = −3: −2 and −1, because −2 × (−1) = 2 and −2 + (−1) = −3. So x² − 3x + 2 = (x − 2)(x − 1). Keep the GCF in front: 4x² − 12x + 8 = 4(x − 2)(x − 1).
💡 How to solve: Factoring ax² + bx + c Completely (GCF First)
First take out the greatest common factor of all three terms. Then factor the trinomial left in the brackets: find two numbers that multiply to ac and add to b, split the middle term, and factor by grouping. Keep the GCF in front of the answer.
Try a similar one
Factor completely: 4x² - 16x + 12
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The GCF of 3, 24 and 45 is 3, so 3x² + 24x + 45 = 3(x² + 8x + 15). Now factor x² + 8x + 15. Find two numbers that multiply to c = 15 and add to b = 8: 5 and 3, because 5 × 3 = 15 and 5 + 3 = 8. So x² + 8x + 15 = (x + 5)(x + 3). Keep the GCF in front: 3x² + 24x + 45 = 3(x + 5)(x + 3).
✓ Correct!
Not quite. The answer is
💡 The GCF of 3, 24 and 45 is 3, so 3x² + 24x + 45 = 3(x² + 8x + 15). Now factor x² + 8x + 15. Find two numbers that multiply to c = 15 and add to b = 8: 5 and 3, because 5 × 3 = 15 and 5 + 3 = 8. So x² + 8x + 15 = (x + 5)(x + 3). Keep the GCF in front: 3x² + 24x + 45 = 3(x + 5)(x + 3).
💡 How to solve: Factoring ax² + bx + c Completely (GCF First)
First take out the greatest common factor of all three terms. Then factor the trinomial left in the brackets: find two numbers that multiply to ac and add to b, split the middle term, and factor by grouping. Keep the GCF in front of the answer.
Try a similar one
Factor completely: 2x² - 2x - 12
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The GCF of 3, 15 and 18 is 3, so 3x² + 15x + 18 = 3(x² + 5x + 6). Now factor x² + 5x + 6. Find two numbers that multiply to c = 6 and add to b = 5: 3 and 2, because 3 × 2 = 6 and 3 + 2 = 5. So x² + 5x + 6 = (x + 3)(x + 2). Keep the GCF in front: 3x² + 15x + 18 = 3(x + 3)(x + 2).
✓ Correct!
Not quite. The answer is
💡 The GCF of 3, 15 and 18 is 3, so 3x² + 15x + 18 = 3(x² + 5x + 6). Now factor x² + 5x + 6. Find two numbers that multiply to c = 6 and add to b = 5: 3 and 2, because 3 × 2 = 6 and 3 + 2 = 5. So x² + 5x + 6 = (x + 3)(x + 2). Keep the GCF in front: 3x² + 15x + 18 = 3(x + 3)(x + 2).
💡 How to solve: Factoring ax² + bx + c Completely (GCF First)
First take out the greatest common factor of all three terms. Then factor the trinomial left in the brackets: find two numbers that multiply to ac and add to b, split the middle term, and factor by grouping. Keep the GCF in front of the answer.
Try a similar one
Factor completely: 2x² + 2x - 4
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The GCF of 4, 36 and 80 is 4, so 4x² + 36x + 80 = 4(x² + 9x + 20). Now factor x² + 9x + 20. Find two numbers that multiply to c = 20 and add to b = 9: 5 and 4, because 5 × 4 = 20 and 5 + 4 = 9. So x² + 9x + 20 = (x + 5)(x + 4). Keep the GCF in front: 4x² + 36x + 80 = 4(x + 5)(x + 4).
✓ Correct!
Not quite. The answer is
💡 The GCF of 4, 36 and 80 is 4, so 4x² + 36x + 80 = 4(x² + 9x + 20). Now factor x² + 9x + 20. Find two numbers that multiply to c = 20 and add to b = 9: 5 and 4, because 5 × 4 = 20 and 5 + 4 = 9. So x² + 9x + 20 = (x + 5)(x + 4). Keep the GCF in front: 4x² + 36x + 80 = 4(x + 5)(x + 4).
💡 How to solve: Factoring ax² + bx + c Completely (GCF First)
First take out the greatest common factor of all three terms. Then factor the trinomial left in the brackets: find two numbers that multiply to ac and add to b, split the middle term, and factor by grouping. Keep the GCF in front of the answer.
Try a similar one
Factor completely: 3x² - 9x - 12
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Factoring ax² + bx + c Completely (GCF First) — Easy Worksheet 2
Factor completely. Take out the GCF first, then factor what is left, like 2(3x - 1)(x + 4).