Factoring Trinomials

Factoring Trinomials Factoring trinomials - Factors of trinomial expressions when the coefficient of the highest power is not unity. Example 1.Resolve into factors 7 x2 - 19x 6. First trial, write down (7x 3) (x 2) noticing that 3 and 2 must have opposite signs. These factors give 7 x2, and 6 for the first and third terms but since 7 X 2 3 X 1 = 11, the combination fails to give the correct coefficient of the middle term. Next try, (7x, 2) (x, 3). Since 7 X 3 2 X 1 = 19 these factors will be correct. If we insert the signs so that the negative shall become predominate. Thus 7 x2 - 19x 6 = 7 x2 21x + 2x 6 = 7x (x 3) + 2 (x 3) = (x 3) (7x + 2) Example 2. Resolve into factors x2 3 x - 54. In the given equation the third term is negative. The second terms of the factors must be such that their product us 54 and their algebraic sum - 3. Hence they must have opposite signs, and the greater of them must be negative in order to give its sign to their sum x2 - 3x 54 = x2 - 9x + 6x 54 Or = x (x - 9) + 6 (x - 9) = x2 - 3x 54 = (x - 9) (x + 6) Example 3. Resolve into factors x2 - 10x + 24. The second term of the factors must be such that their product is + 24 and their sum -10, it is clear that they must be - 6 and - 4. x2 - 10x + 24 = x2 - 6 x - 4 x + 24 = x (x - 6) - 4 (x - 6) Or x2 - 10x + 24 = (x - 6) (x - 4)