# Worksheet on Factoring Trinomials | Factoring Trinomials Worksheet with Answers

Take the help of Worksheet on Factoring Trinomials and practice well for the exam. It’s really easy for all the students to score good marks in the exam if they practice with Factoring Trinomials Worksheets. Allot your time to practice all problems available on the Factoring Trinomials Practice Worksheets to improve your subject knowledge. You can easily clear all of your doubts by taking the reference of our Factorization Worksheets. Immediately begin your practice and become an expert in solving Factorization Problems.

1. Factor trinomials of the form ax² + bx + c

(i) 2a2 + 11a + 12
(ii) 3a2 + 8a + 4
(iii) 3a2 – 13a + 14
(iv) 4a2 – 7a + 3
(v) 5a2 – 11a – 12
(vi) 7a2 – 15a – 18

Solution:

(i) The given expression 2a2 + 11a + 12
Rewrite the equation
2a2 + 8a + 3a + 12
Group the first two terms and last two terms.
The first two terms are 2a2 + 8a and the second two terms are 3a + 12.
Take 2a common from the first two terms.
2a (a + 4)
Take 3 common from the second two terms.
3 (a + 4)
2a (a + 4) + 3 (a + 4)
Then, take (a + 4) common from the above expression.
(a + 4) (2a + 3)

The final answer is (a + 4) (2a + 3).

(ii) The given expression 3a2 + 8a + 4
Rewrite the equation
3a2 + 6a + 2a + 4
Group the first two terms and last two terms.
The first two terms are 3a2 + 6a and the second two terms are 2a + 4.
Take 3a common from the first two terms.
3a (a + 2)
Take 2 common from the second two terms.
2 (a + 2)
3a (a + 2) + 2 (a + 2)
Then, take (a + 2) common from the above expression.
(a + 2) (3a + 2)

The final answer is (a + 2) (3a + 2).

(iii) The given expression 3a2 – 13a + 14
Rewrite the equation
3a2 – 6a – 7a + 14
Group the first two terms and last two terms.
The first two terms are 3a2 – 6a and the second two terms are – 7a + 14.
Take 3a common from the first two terms.
3a (a – 2)
Take -7 common from the second two terms.
-7 (a – 2)
3a (a – 2) – 7 (a – 2)
Then, take (a – 2) common from the above expression.
(a – 2) (3a – 7)

The final answer is (a – 2) (3a – 7).

(iv) The given expression 4a2 – 7a + 3
Rewrite the equation
4a2 – 4a – 3a + 3
Group the first two terms and last two terms.
The first two terms are 4a2 – 4a and the second two terms are – 3a + 3.
Take 4a common from the first two terms.
4a (a – 1)
Take -3 common from the second two terms.
-3 (a – 1)
4a (a – 1) – 3 (a – 1)
Then, take (a – 1) common from the above expression.
(a – 1) (4a – 3)

The final answer is (a – 1) (4a – 3).

(v) The given expression 5a2 – 11a – 12
Rewrite the equation
5a2 – 15a + 4a – 12
Group the first two terms and last two terms.
The first two terms are 5a2 – 15a and the second two terms are 4a – 12.
Take 4a common from the first two terms.
5a (a – 3)
Take 4 common from the second two terms.
4 (a – 3)
5a (a – 3) + 4 (a – 3)
Then, take (a – 3) common from the above expression.
(a – 3) (5a + 4)

The final answer is (a – 3) (5a + 4).

(vi) The given expression 7a2 – 15a – 18
Rewrite the equation
7a2 – 21a + 6a – 18
Group the first two terms and last two terms.
The first two terms are 7a2 – 21a  and the second two terms are 6a – 18.
Take 7a common from the first two terms.
7a (a – 3)
Take 6 common from the second two terms.
6 (a – 3)
7a (a – 3) + 6 (a – 3)
Then, take (a – 3) common from the above expression.
(a – 3) (7a + 6)

The final answer is (a – 3) (7a + 6).

2. Factor trinomials

(i) 7a2 + 6a – 1
(ii) 9a2 + 35a – 4
(iii) 2a2 – 5a + 3
(iv) 7a – 6 – 2a2
(v) 11a2 – 54a + 63
(vi) a2 + 2a – 3

Solution:

(i) The given expression 7a2 + 6a – 1
Rewrite the equation
7a2 + 7a – a – 1
Group the first two terms and last two terms.
The first two terms are 7a2 + 7a and the second two terms are – a – 1.
Take 7a common from the first two terms.
7a (a + 1)
Take -1 common from the second two terms.
-1 (a + 1)
7a (a + 1) – 1 (a + 1)
Then, take (a + 1) common from the above expression.
(a + 1) (7a – 1)

The final answer is (a + 1) (7a – 1).

(ii) The given expression 9a2 + 35a – 4
Rewrite the equation
9a2 + 36a – a – 4
Group the first two terms and last two terms.
The first two terms are 9a2 + 36a and the second two terms are – a – 4.
Take 9a common from the first two terms.
9a (a + 4)
Take -1 common from the second two terms.
-1 (a + 4)
9a (a + 4) – 1 (a + 4)
Then, take (a + 4) common from the above expression.
(a + 4) (9a – 1)

The final answer is (a + 4) (9a – 1).

(iii) The given expression 2a2 – 5a + 3
Rewrite the equation
2a2 – 2a – 3a + 3
Group the first two terms and last two terms.
The first two terms are 2a2 – 2a and the second two terms are – 3a + 3.
Take 2a common from the first two terms.
2a (a – 1)
Take -3 common from the second two terms.
-3 (a – 1)
2a (a – 1) – 3 (a – 1)
Then, take (a – 1) common from the above expression.
(a – 1) (2a – 3)

The final answer is (a – 1) (2a – 3).

(iv) The given expression 7a – 6 – 2a2
Rewrite the equation
– 2a2 + 4a + 3a – 6
Group the first two terms and last two terms.
The first two terms are – 2a2 + 4a and the second two terms are 3a – 6.
Take -2a common from the first two terms.
-2a (a – 2)
Take 3 common from the second two terms.
3 (a – 2)
-2a (a – 2) + 3 (a – 2)
Then, take (a – 2) common from the above expression.
(a – 2) (-2a + 3)

The final answer is (a – 2) (-2a + 3).

(v) The given expression 11a2 – 54a + 63
Rewrite the equation
11a2 – 33a – 21a + 63
Group the first two terms and last two terms.
The first two terms are 11a2 – 33a and the second two terms are – 21a + 63.
Take 11a common from the first two terms.
11a (a – 3)
Take -21 common from the second two terms.
-21 (a – 3)
11a (a – 3) – 21 (a – 3)
Then, take (a – 3) common from the above expression.
(a – 3) (11a – 21)

The final answer is (a – 3) (11a – 21).

(vi) The given expression a2 + 2a – 3
Rewrite the equation
a2 + 3a – a – 3
Group the first two terms and last two terms.
The first two terms are a2 + 3a and the second two terms are – a – 3.
Take a common from the first two terms.
a (a + 3)
Take -1 common from the second two terms.
-1 (a + 3)
a (a + 3) – 1 (a + 3)
Then, take (a + 3) common from the above expression.
(a + 3) (a – 1)

The final answer is (a + 3) (a – 1).

(i) 2x2 + 5x + 2
(ii) 3a2 + 14a + 8
(iii) 2x2 + 7x + 6
(iv) 6a2 – a – 15
(v) 9s2 – s – 8
(vi) 12 + a – 6a2
(vii) 6 + 5x – 6x2
(viii) a2 + 8a – 105

Solution:

(i) The given expression 2x2 + 5x + 2
Rewrite the equation
2x2 + 4x + x + 2
Group the first two terms and last two terms.
The first two terms are 2x2 + 4x and the second two terms are x + 2.
Take 2x common from the first two terms.
2x (x + 2)
Take 1 common from the second two terms.
1 (x + 2)
2x (x + 2) + 1 (x + 2)
Then, take (x + 2) common from the above expression.
(x + 2) (2x + 1)

The final answer is (x + 2) (2x + 1).

(ii) The given expression 3a2 + 14a + 8
Rewrite the equation
3a2 + 12a + 2a + 8
Group the first two terms and last two terms.
The first two terms are 3a2 + 12a and the second two terms are 2a + 8.
Take 3a common from the first two terms.
3a (a + 4)
Take 2 common from the second two terms.
2 (a + 4)
3a (a + 4) + 2 (a + 4)
Then, take (a + 4) common from the above expression.
(a + 4) (3a + 2)

The final answer is (a + 4) (3a + 2).

(iii) The given expression 2x2 + 7x + 6
Rewrite the equation
2x2 + 4x + 3x + 6
Group the first two terms and last two terms.
The first two terms are 2x2 + 4x and the second two terms are 3x + 6.
Take 2x common from the first two terms.
2x (x + 2)
Take 3 common from the second two terms.
3 (x + 2)
2x (x + 2) + 3 (x + 2)
Then, take (x + 2) common from the above expression.
(x + 2) (2x + 3)

The final answer is (x + 2) (2x + 3).

(iv) The given expression 6a2 – a – 15
Rewrite the equation
6a2 + 9a -10a  – 15
Group the first two terms and last two terms.
The first two terms are 6a2 + 9a and the second two terms are -10a  – 15.
Take 3a common from the first two terms.
3a (2a + 3)
Take -5 common from the second two terms.
-5 (2a + 3)
3a (2a + 3) -5 (2a + 3)
Then, take (2a + 3) common from the above expression.
(2a + 3) (3a – 5)

The final answer is (2a + 3) (3a – 5).

(v) The given expression 9s2 – s – 8
Rewrite the equation
9s2 – 9s + 8s – 8
Group the first two terms and last two terms.
The first two terms are 9s2 – 9s and the second two terms are 8s – 8.
Take 9s common from the first two terms.
9s (s – 1)
Take 8 common from the second two terms.
8 (s – 1)
9s (s – 1) + 8 (s – 1)
Then, take (s – 1) common from the above expression.
(s – 1) (9s + 8)

The final answer is (s – 1) (9s + 8).

(vi) The given expression 12 + a – 6a2
Rewrite the equation
– 6a2 + 9a -8a + 12
Group the first two terms and last two terms.
The first two terms are – 6a2 + 9a and the second two terms are -8a + 12 .
Take -3a common from the first two terms.
-3a (2a – 3)
Take -4 common from the second two terms.
-4 (2a – 3)
-3a (2a – 3) – 4 (2a – 3)
Then, take (2a – 3) common from the above expression.
(2a – 3) (-3a – 4)

The final answer is (2a – 3) (-3a – 4).

(vii) The given expression 6 + 5x – 6x2
Rewrite the equation
– 6x2 + 9x – 4x +6
Group the first two terms and last two terms.
The first two terms are – 6x2 + 9x and the second two terms are – 4x +6.
Take -3x common from the first two terms.
-3x (2x – 3)
Take -2 common from the second two terms.
-2 (2x – 3)
-3x (2x – 3) -2 (2x – 3)
Then, take (2x – 3) common from the above expression.
(2x – 3) (-3x – 2)

The final answer is (2x – 3) (-3x – 2).

(viii) The given expression a2 + 8a – 105
Rewrite the equation
a2 + 15a – 7a – 105
Group the first two terms and last two terms.
The first two terms are a2 + 15a and the second two terms are – 7a – 105.
Take a common from the first two terms.
a (a + 15)
Take -7 common from the second two terms.
-7 (a + 15)
a (a + 15) – 7 (a + 15)
Then, take (a + 15) common from the above expression.
(a + 15) (a – 7)

The final answer is (a + 15) (a – 7).