FACTORIZATION - USING PRODUCT AND SUM

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 FACTORIZATION - USING PRODUCT AND SUM



EXAMPLE 1

Factorize: X2 + 8x + 15

 a= 1, b = 8, c = 15

 Product = a × c

               = 1 × 15

                = 15

Sum = b

         = 8

 To get the product 15 we can multiply 3 and 5 and to get the sum of 15 we can add 3 and 5.

Therefore, the middle term 8x can be written as 3x + 5x.

 X2 + 8x + 15 =  X2 + 3x + 5x + 15

                     = (x2 + 3x) + (5x + 15)

                      = x(x + 3) + 5(x + 3)

                      = (x + 5) (x + 3) are the two factors

EXAMPLE 2

Factorize: 7X2 + 2x - 5

 a= 7, b = 2, c = -5

 Product = a × c

               = 7× -5

                = -35

 Sum = b

         = 2

 To get the product -35 we can multiply -5 and 7 and to get the sum of 15 we can add -5 and 7.

Therefore, the middle term 2x can be written as -5x + 7x.

 7X2 + 2x – 5 =  7X2 – 5x + 7x -5

                     = (7X2 + 7x) – ( 5X+ 5)

                      = 7X(X + 1) – 5(X +1)

                      = (7X – 5)(X+1)  are the two factors


EXAMPLE 3

Factorize: 3X2 - 5x + 2

 a= 3, b = -5, c = 2

 Product = a * c

               = 3* 2

                = 6

Sum = b

         = -5

 To get the product 6 we can multiply -3 and -2 and to get the sum of -5 we can add -3 and -2.

Therefore, the middle term -5x  can be written as -3x - 2x.

 3X2 - 5x + 2 = 3X2 -3x -2x +2

                      = (3X2 -3x)+(-2x+2)

                       = 3x(x-1) -2(x – 1)

                       = (3x-2)(x-1) are the two factors

EXAMPLE 4

Factorize: 2X2 - 3x - 2

 a= 2, b = -3, c = -2

Product = a × c

               = 2×-2

                = -4

 Sum = b

         = -3

 To get the product -4 we can multiply -4 and  1 and to get the sum of -3 we can add -4 and  1.

Therefore, the middle term -3x  can be written as -4x + x.

 2X2 - 3x – 2 = 2X2 -4x + x – 2

                     = (2X2 + x) – (4x + 2)                     

                     =  x(2x + 1) – 2(2x + 1)

                    = (2x+1)(x-2) are the factors


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