Worksheet on Factoring Trinomials by Substitution
Practice the worksheet on factoring trinomials by substitution. We know how to factor trinomial of the form x
^{2} + bx + c or ax
^{2} + bx + c.
But when a given trinomial does not fit in the form of x
^{2} + bx + c or ax
^{2} + bx + c in such cases we need substitute it to get in the form x
^{2} + bx + c or ax
^{2} + 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) (x
^{2} - 3x)
^{2} – 38(x
^{2} -3x) - 80
(vi) 6(x – y)
^{2} – x + y – 15
(vii) (p
^{2} – 3q
^{2})
^{2} – 16(p
^{2} – 3q
^{2}) + 63
(viii) (m
^{2} + 2m)
^{2} – 21(m
^{2} + 2m) – 72
(ix) (x
^{2} – 8x)
^{2} – 29(x
^{2} – 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) (p
^{2} – 3q
^{2} – 7)(p
^{2} – 3q
^{2} - 9)
(viii) (m
^{2} + 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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