To Factor the form :ax^{2} + bx + c | Factor : 6x^{2} + 19x + 10 |
1) Find the product of 1st and last term( a x c). | 6 x 10 = 60 |
2) Find the factors of 60 in such way that addition or subtraction of that factors is the middle term (19x)(Splitting of middle term) |
15 x 4 = 60 and 15 + 4 = 19 |
3) Write the center term using the sum of the two new factors, including the proper signs. |
6x^{2} + 15x + 4x + 10 |
4) Group the terms to form pairs - the first
two terms and the last two terms. Factor each pair by finding common factors. |
3x ( 2x + 5)+ 2(2x + 5) |
5) Factor out the shared (common) binomial parenthesis. | (3x + 2) ( 2x + 5) |
Example: Find the factors of 6x^{2} - 13x + 6 6x^{2} - 13 x + 6 ----->(1) a.c = Product of 6 and 6 = 36 Factors of 36 = 2,18 = 3,12 = 4,9 Only the factors 4 and 9 gives 13-->(4 + 9) For -13 , both the factors have negative sign. – 4 – 9 = - 13 Equation (1) ⇒ 6x ^{2} - 4x – 9x + 6 ⇒2x ( 3x – 2 ) – 3 ( 3x – 2 ) ⇒(3x – 2 ) ( 2x – 3) are the factors. |