# Factoring trinomials worksheet (solved examples)

# Factorise the following Quadratic trinomials by spiliting the middle terms.

We know, in order to factorise the expression ax^{2} + bx + c, we have to find two numbers p and q, such that p + q = b and p × q = ac. |

**Example 1: Factorise**

Solution. Find two factors p and q such that p+q=-7 and pq =12 . Take p=-3 and q=-4 then 12= -3 x (-4) and -3-4=-7 .

Therefore =

=

=

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**Example 2: Obtain the factors of **

**.**

Solution. ** = **

=

=

**Example 3: Find the factors of .**

Solution. Note that 3 is common factor in all the terms. Therefore

**=**

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=

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**Example 4: Factorise** .

Solution. We split

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Hence =

**Example 5: Factorise .**

Sol. Here , 9 x 8 =72. We spilt -22 into parts whose sum is-22 and product 72 .

Clearly , (-18)+(-4) =-22 and (-18) x (-4)=72 .

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=

Hence **= **

**Example 6: ****Factorise .**

Sol. Here ,

Clearly , (-2)+(-45) =-47 and (-2) x (-45)=90 .

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Hence

**= .**

**Example 7: ****Factorise **

**.**

Solution : Here, . We split

Clearly, and

** = **

=

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Hence ** = **

**.**

**Example 8: Factorise** .

Solution: The given expression is

Here , .

So, we split -10 in two parts whose sum is -10 and product -56.

Clearly, (-14+4) =-10 and (-14) x 4 =-56.

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**Factoring trinomials worksheet PDF download**

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