Factorization by grouping the terms Factorization by Grouping
Factorization by grouping the terms
Factorization by Grouping the terms… Eg 1. X³ - 2 x² + x – 2 [step 1: In first two terms x² is common In second term 1 is common - lets take out those 2 term] X³ - 2 x² + x – 2 =x² (x) - x²(2) + 1(x) – 1(2) = x²(x -2) + 1(x - 2) [step 2: let’s group the common term from the both first and second term (i. e) (x – 2), then group the remaining terms in another group] x²(x -2) + 1(x - 2) = (x² + 1) (x – 2)
Factorization by Grouping the terms… Eg 2. y³ + 3 y + y 2 + 3 [step 1: In first two terms y is common In second term 1 is common - lets take out those 2 term] y³ + 3 y + y 2 + 3 =y(y 2) + y(3) + 1(y 2) + 1(3) = y(y 2 + 3) + 1(y 2 + 3) [step 2: let’s group the common term from the both first and second term (i. e) (y 2 + 3), then group the remaining terms in another group] y(y 2 + 3) + 1(y 2 + 3) = (y + 1) (y 2 + 3)
Factorization by Grouping the terms… Eg 3. 4 x 2 + 20 x – 3 xy – 15 y [step 1: In first two terms 4 x is common In second term -3 y is common - lets take out those 2 term] 4 x 2 + 20 x – 3 xy – 15 y =4 x(x) + 4 x(5) – 3 y(x) – 3 y(5) = 4 x(x + 5) -3 y(x + 5) [step 2: let’s group the common term from the both first and second term (i. e) (x + 5), then group the remaining terms in another group] 4 x(x + 5) -3 y(x + 5) = (4 x – 3 y) (x + 5)
Try These Factorize the following: 1. m 2 + 3 m + 5 m + 15 2. 4 x 2 + 6 xy – 8 xy – 12 y 2
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