factoring using the quadratic formulaFactoring using the quadratic formula is the goal of this lesson. It is closely related to solving equations using the quadratic formula 2 easy steps to follow when factoring using the quadratic formula: Step #1: Solve the quadratic equation to get x_{1} and x_{2} Step #2 Uisng the answers found in step #1, the factorization form is a (x  x_{1})(x  x_{2}) Example #1: Factor 4x^{2} + 9x + 2 = 0 using the quadratic formula. a = 4, b = 9, and c = 2 x = (b ± √(b^{2}  4ac)) / 2a x = (9 ± √(9^{2}  4 × 4 × 2)) / 2 × 4 x = (9 ± √(81  4 × 4 × 2)) / 8 x = (9 ± √(81  4 × 8)) / 8 x = (9 ± √(81  32)) / 8 x = (9 ± √(49)) / 8 x = (9 ± 7 ) / 8 x_{1} = (9 + 7 ) / 8 x_{1} = (2 ) / 8 x_{1} = 1/4 x_{2} = (9  7 ) / 8 x_{2} = (16 ) / 8 x_{2} = 2 The factorization form is a (x  x_{1})(x  x_{2}) The factorization form is 4 (x  1/4)(x  2) The factorization form is 4 (x + 1/4)(x + 2) Now, use distributive property to simplify the expression by getting rid of fractions 4 (x + 1/4)(x + 2) = (4 × x + 4 × 1/4) (x + 2) = (4x + 1)(x + 2) Example #2: Factor x^{2} + 2x  15 = 0 using the quadratic formula a = 1, b = 2, and c = 15 x = (b ± √(b^{2}  4ac)) / 2a x = ( 2 ± √(2^{2}  4 × 1 × 15)) / 2 × 1 x = (2 ± √(4  4 × 1 × 15)) / 2 x = (2 ± √(4  4 × 15)) / 2 x = (2 ± √(4 + 60)) / 2 x = (2 ± √(64)) / 2 x = (2 ± 8 ) / 2 x_{1} = (2 + 8 ) / 2 x_{1} = ( 6 ) / 2 x_{1} = 3 x_{2} = (2  8 ) / 2 x_{2} = (10) / 2 x_{2} = 5 The factorization form is a (x  x_{1})(x  x_{2}) The factorization form is 1 (x  3)(x  5) The factorization form is 1 (x  3)(x + 5) Now, use distributive property to simplify the expression 1 (x  3)(x + 5) = (1 × x + 1 × 3) (x + 2) = (x  3)(x + 5) It is important to understand how to use the quadratic formula before fatoring using the quadratic formula. 




