October 7, 2022

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

 We know, in order to factorise the expression ax2 + bx + c, we have to find two numbers p and q, such that p + q = b and p × q = ac.

Example 1: Factorise

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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.  =

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Example 3: Find the factors of .

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

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Example 4: Factorise .

Solution.  We split into two parts whose sum is and product is 12. Clearly and

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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 , . We spilt -47 into two parts whose sum is-47 and product 90 .

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

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Hence = .

Example 7: Factorise .

Solution : Here,   . We split into two parts whose sum is and product .

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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