Factoring

Factoring Trinomials of the Form 5.3 Factoring Trinomials of the Form ax2 + bx + c, a = 1

Factoring Trinomials Recall that factoring is the reverse process of multiplication. Using the FOIL method, we can show that (x + 3)(x + 4) = x2 + 7x + 12. Therefore x2 + 7x + 12 = (x + 3)(x + 4) Note that this trinomial results in the product of two binomials whose first term is x and second term is a number (including its sign).

Factoring Trinomials Factoring any polynomial of the form x2 + bx + c will result in a pair of binomials: Numbers go here. x2 + bx + c = (x +?)(x +?) O ( x + 3 )( x + 4 ) F I L = x2 + 4x + 3x + 12 = x2 + 7x + 12

Factoring Trinomials Factor out a GCF if possible. Find two numbers whose product equals the constant, c, and whose sum equals the coefficient of the x-term, b. Use the two numbers found in step 2, including their signs, to write the trinomial in factored form. Check using FOIL.

Examples – Factor each. x2 – 5x + 6 x2 + 2xy + y2 x2 + 8x + 15