The equation which is in the form of ax² + bx + c known as quadratic equation.In which a ≠ 0.

To factor any quadratic equation, first we have to check whether the coefficient of x² is 1 or not.

• If it is one then we can just take the last term and split this term as two parts.
• If it is not 1 we have to multiply the coefficient of x² by the constant term and split this number as two parts.
• The signs of two factors is depending on the given quadratic equation.

Example 1 :

Factorize x² + 15 x + 14

Solution :

Now we have to split the last term 14 as two parts, the product of those parts must be equal to the last term (14)  and simplified value must be equal to the middle term (15).

Since the quadratic equation in the form of  ax² + b x + c, we have to put positive sign for both factors.

Hence the factors of the quadratic equation  x²+15 x+14 are (x + 1) (x + 14)

Example 2 :

Factorize x² + 13 x + 30

Solution :

Now we have to split the last term 30 as two parts, the product of those parts must be equal to the last term (30)  and simplified value must be equal to the middle term (13).

Since the quadratic equation in the form of  ax² + b x + c, we have to put positive sign for both factors.

Hence the factors of the quadratic equation  x²+13x+30 are (x + 10) (x + 3)

Example 3 :

Factorize x² - 14 x + 24

Solution :

Now we have to split the last term 24 as two parts, the product of those parts must be equal to the last term (24)  and simplified value must be equal to the middle term (14).

Since the quadratic equation in the form of  ax² + b x + c, we have to put positive sign for both factors.

Hence the factors of the quadratic equation  x²-14x+24 are (x-12) (x-2)

Example 4 :

Factorize x² - 16 x + 60

Solution :

Now we have to split the last term 60 as two parts, the product of those parts must be equal to the last term (60)  and simplified value must be equal to the middle term (-16).

Since the quadratic equation in the form of  ax² - b x + c, we have to put positive sign for both factors.

Hence the factors of the quadratic equation  x²-16x+60 are (x-10) (x-6)

Example 5 :

Factorize x² - 2 x - 99

Solution :

Now we have to split the last term -99 as two parts, the product of those parts must be equal to the last term (-99)  and simplified value must be equal to the middle term (-2).

Since the quadratic equation in the form of  ax² - b x - c, we have to take negative sign for big number.

Hence the factors of the quadratic equation  x²-2x-99 are (x-11) (x+9)

Example 6 :

Factorize 3x² + 19 x + 6

Solution :

Since the coefficient of x² is not 1, we have to multiply the coefficient of x² by the constant term, then  we have to split this number as two parts.

Since the quadratic equation in the form of  ax² + b x + c, we have to take negative sign for big number.

Hence the factors of the quadratic equation  3x²+19x+6 are (3x+1) (x+6)

After having gone through the stuff given above, we hope that the students would have understood "Factor quadratics".

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