Worksheet on Factorization of the Trinomial ax^2 + bx + c | Free Factoring Trinomial ax^2 + bx + c Worksheet

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Also, See:

• Problems on Factorization of Expressions of the Form x² +(a + b)x +ab
• Factorization of Expressions of the Form ax² + bx + c, a ≠ 1

Free Factoring Trinomial Worksheet PDF

Example 1.
Factor the Trinomial 2b² + 11b + 12?
Solution:
Given Expression = 2b² + 11b + 12
= 2b² + 8b+3b + 12
=2b(b+4)+3(b+4)
=(2b+3)(b+4)

Example 2.
Factorize x² + 8x – 105?
Solution:
Given Expression = x² + 8x – 105
= x² + 15x –7x-105
=x(x+15)-7(x+15)
=(x-7)(x+15)

Example 3.
Factorize 9c² – c – 8?
Solution:
Given Expression = 9c² – c – 8
=9c² – 9c+8c – 8
=9c(c-1)+8(c-1)
=(9c+8)(c-1)

Example 4.
Factorize Trinomial 7m² – 15m – 18?
Solution:
Given Expression = 7m² – 15m – 18
=7m² – 21m+6m – 18
=7m(m-3)+6(m-3)
=(7m+6)(m-3)

Example 5.
Factorize the Trinomial 18 + 11x + x²
Solution:
Given Expression = 18 + 11x + x²
=18+9x+2x+x²
=x(x+9)+2(x+9)
=(x+9)(x+2)

Example 6.
Factorize 5p²+ 19 p + 12
Solution:
Given Expression = 5p²+ 19 p + 12
=5p²+ 15p +4p+ 12
=5p(p+3)+4(p+3)
=(5p+4)(p+3)

Example 7.
Factorize 6r²− 17r + 12?
Solution:
Given Expression = 6r²− 17r + 12
=6r²− 17r + 12
=6r²− 8r-9r + 12
=2r(3r-4)-3(3r-4)
=(3r-4)(2r-3)

Example 8.
Factorize 3r²+ 40r + 100
Solution:
Given Expression = 3r²+ 40r + 100
=3r²+ 40r + 100
=3r²+ 30r +10r+ 100
=3r(r+10)+10(r+10)
=(3r+10)(r+10)