Worksheet on Factoring Trinomials
Practice the worksheet on factoring trinomials to know how to factorize the quadratic expression of the form ax
^{2} + bx + c. We know, in order to factorize the expression ax
^{2} + bx + c, we have to find two numbers p and q, such that p + q = b and p × q = ac.
1. Factoring trinomials of the form ax^{2} + bx + c:
(i) 2m
^{2} + 11m + 12
(ii) 3m
^{2} + 8m + 4
(iii) 3m
^{2} - 13m + 14
(iv) 4m
^{2} - 7m + 3
(v) 5m
^{2} - 11m - 12
(vi) 7m
^{2} - 15m – 18
2. Factor trinomials:
(i) 7m
^{2} + 6m – 1
(ii) 9m
^{2} + 35m – 4
(iii) 2m
^{2} - 5m + 3
(iv) 7m - 6 - 2m
^{2}
(v) 11m
^{2} - 54m + 63
(vi) m
^{2} + 2m – 3
3. Factorize the quadratic expression:
(i) 2a
^{2} + 5a + 2
(ii) 3x
^{2} + 14x + 8
(iii) 2m
^{2} + 7m + 6
(iv) 6x
^{2} – x - 15
(v) 9r
^{2} – r - 8
(vi) 12 + x - 6x
^{2}
(vii) 6 + 5a – 6a
^{2}
(viii) x
^{2} + 8x – 105
Answers for the worksheet on
factoring trinomials are given below to check the exact answers of the above
quadratic expression.
Answers:
1. (i) (2m + 3)(m + 4)
(ii) (3m + 2)(m + 2)
(iii) (m - 2)(3m – 7)
(iv) (4m - 3)(m – 1)
(v) (5m + 4)(m – 3)
(vi) (7m + 6)(m – 3)
2. (i) (7m – 1)(m + 1)
(ii) (m + 4)(9m - 1)
(iii) (2m - 3)(m – 1)
(iv) (3 – 2m)(m – 2)
(v) (11m - 21)(m – 3)
(vi) (m + 3)(m – 1)
3. (i) (a + 2)(2a
+ 1)
(ii) (x + 4)(3x + 2)
(iii) (m + 2)(2m + 3)
(iv) (2x + 3)(3x - 5)
(v) (r – 1)(9r + 8)
(vi) (3 – 2x)(4 + 3x)
(vii) (3 – 2a)(2 + 3a)
(viii) (x + 15)(x – 7)
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