Worksheet on Factoring Trinomials by Substitution

Practice the worksheet on factoring trinomials by substitution. We know how to factor trinomial of the form x² + bx + c or ax² + bx + c.

But when a given trinomial does not fit in the form of x² + bx + c or ax² + bx + c in such cases we need substitute it to get in the form x² + bx + c or ax² + bx + c.

1. Factor the following trinomials using the substitution method:

(i) 4(a – b)² – 14(a – b) - 8

(ii) 3(3x + 2)² + 5(3x + 2) - 2

(iii) 2(a + 2b)² + (a + 2b) - 1

(iv) (a + b)² - (a + b) - 6



(v) (x² - 3x)² – 38(x² -3x) - 80

(vi) 6(x – y)² – x + y – 15

(vii) (p² – 3q²)² – 16(p² – 3q²) + 63

(viii) (m² + 2m)² – 21(m² + 2m) – 72

(ix) (x² – 8x)² – 29(x² – 8x) + 180

(x) (x + y)² – 8x - 8y + 7



2. Factor trinomials using substitution:

(i) (x – 2y)² + 7(x – 2y) - 18

(ii) 3(a – b)² – (a – b) - 44

(iii) (5a – 3b)² + 8(5a – 3b) + 16

(iv) (x – 4y)² - 10(x – 4y) + 25

(v) (3r – 4)² - 4(3r – 4) - 12

(vi) (7m – 1)² + 12(7m – 1) – 45

Answers for the worksheet on factoring trinomials by substitution are given below to check the exact answers of the above trinomial expressions.

Answers:

1. (i) 2(a – b – 4)(2a – 2b + 1)

(ii) (3x – 4)(9x + 5)

(iii) (a + 2b + 1)(2a + 4b – 1)

(iv) (a + b – 3)( a + b + 2)

(v) (x - 8)(x + 5)(x - 2)(x - 1)

(vi) (2x - 2y + 3)(3x - 3y - 5)

(vii) (p² – 3q² – 7)(p² – 3q² - 9)

(viii) (m² + 2m + 3)(m – 4)(m + 6)

(ix) (x – 10)(x + 2)(x – 9)(x + 1)

(x) (x + y – 7)(x + y – 1)

2. (i) (x – 2y + 9)(x – 2y – 2)

(ii) (a – b – 4)(3a – 3b + 11)

(iii) (5a - 3b + 4)(5a - 3b + 4)  

(iv)  (x – 4y – 5)(x – 4y – 5)   

(v)  (3r – 2)(3r - 10)

(vi) 7(7m – 4)(m + 2)

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