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Also, See:

- Problems on Factorization of Expressions of the Form x
^{2}+(a + b)x +ab - Factorization of Expressions of the Form ax
^{2}+ bx + c, a ≠ 1

## Free Factoring Trinomial Worksheet PDF

**Example 1.
**Factor the Trinomial 2b

^{2}+ 11b + 12?

**Solution:**

Given Expression = 2b

^{2}+ 11b + 12

= 2b

^{2}+ 8b+3b + 12

=2b(b+4)+3(b+4)

=(2b+3)(b+4)

**Example 2.
**Factorize x

^{2}+ 8x – 105?

**Solution:**

Given Expression = x

^{2}+ 8x – 105

= x

^{2}+ 15x –7x-105

=x(x+15)-7(x+15)

=(x-7)(x+15)

**Example 3.
**Factorize 9c

^{2}– c – 8?

**Solution:**

Given Expression = 9c

^{2}– c – 8

=9c

^{2}– 9c+8c – 8

=9c(c-1)+8(c-1)

=(9c+8)(c-1)

**Example 4.
**Factorize Trinomial 7m

^{2}– 15m – 18?

**Solution:**

Given Expression = 7m

^{2}– 15m – 18

=7m

^{2}– 21m+6m – 18

=7m(m-3)+6(m-3)

=(7m+6)(m-3)

**Example 5.
**Factorize the Trinomial 18 + 11x + x

^{2}

**Solution:**

Given Expression = 18 + 11x + x

^{2}

=18+9x+2x+x

^{2}

=x(x+9)+2(x+9)

=(x+9)(x+2)

**Example 6.
**Factorize 5p

^{2}+ 19 p + 12

**Solution:**

Given Expression = 5p

^{2}+ 19 p + 12

=5p

^{2}+ 15p +4p+ 12

=5p(p+3)+4(p+3)

=(5p+4)(p+3)

**Example 7.
**Factorize 6r

^{2}− 17r + 12?

**Solution:**

Given Expression = 6r

^{2}− 17r + 12

=6r

^{2}− 17r + 12

=6r

^{2}− 8r-9r + 12

=2r(3r-4)-3(3r-4)

=(3r-4)(2r-3)

**Example 8.
**Factorize 3r

^{2}+ 40r + 100

**Solution:**

Given Expression = 3r

^{2}+ 40r + 100

=3r

^{2}+ 40r + 100

=3r

^{2}+ 30r +10r+ 100

=3r(r+10)+10(r+10)

=(3r+10)(r+10)