factoring trinomials with coefficients

When the coefficient of the highest power is 1. i.e., ax 2 bx c, when a = 1 and b and c are integers. When two binomials are multiplied the product is a trinomial. Thus (x + 4) (x + 5) = x 2 + 9x + 20 (1) (x - 4) (x - 5) = x 2 - 9x + 20 (2) In this chapter we try t..

The general form of the trinomial is (x 2 + cx + d) where c and d have different numerical values: c = a + b, and d = ab. In these examples, study the relation between the middle and the last terms. Therefore, to factorise expressions of the type (x 2 + cx + d), we have to find two ..

Find all pairs of factors whose product is the last term of the trinomial. From the pairs of factors from step 1, choose a pair of factors whose sum is the coefficient of the middle term of the trinomial. Split the middle term using the..

Factor the trinomial. 72 x 2 + 17 x - 72 => (9 x + 8)(8 x - 9) or (9 x - 8)(8 x + 9) or (8 x - 9)( x + 9) or ( x - 8)(81 x + 64)..

Factor the trinomial: 6 y 2 - 55 y - 50 => ( y - 5)(6 y + 10) or ( y - 10)(6 y + 5) or ( y + 6)(5 y + 5) or ( y - 1)(6 y - 50)..

Factor the trinomial. 7 y 2 - 78 y - 72 => ( y - 6)(7 y + 12) or ( y + 7)(6 y + 6) or ( y - 12)(7 y + 6) or ( y - 1)(7 y - 72)..

Factor the trinomial. 2 x 2 - 5 x y - 12 y 2 => (2 x + 3 y )( x - 4 y ) or (2 x - 3 y )( x - 4 y ) or (2 x + 3 y )( x + 4 y ) or (2 x - 3 y )( x + 4 y )..

Factor the trinomial. 3 x 2 y 2 z 2 + 7 x y z - 20 => (3 x y z - 5)(3 x y z - 4) or (3 x y z + 5)(3 x y z - 4) or (3 x y z + 5)..

By trial and error method, find the factor of the constant for which the given expression becomes equal to zero. Divide the expression by the factor that is determined in step 1. Factorise the quotient. If the quotient is a trinomial, factorise it further. I..

Finding the solution by the method of substitution. (i) Coefficients of one of the variables (say x) in the two equations are made equal, by multiplying them with suitable factors..