Warm-Up Factor the following expressions by pulling out things that each term has in common: 4x3 + 8x2 + 12xz 9x2y3 + 3xy2 + 27xy4

X-box Factoring

Standard Students apply basic factoring techniques to second- and simple third-degree polynomials. These techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials. Objective: We will use the x-box method to factor trinomials.

Factor the x-box way We are going to factor trinomials like 3x2 + 27x + 60 using the X-Box method. Step 1: Write the polynomial in standard form. Step 2: Factor all common factors in the trinomial. Step 3: Use the X method. Step 4: Write your answer. Step 5: Check your answer by distributing

First and Last Coefficients Factor the x-box way y = ax2 + bx + c Product ac=mn First and Last Coefficients n m Middle b=m+n Sum

Examples Factor using the x-box method. 1. x2 + 4x – 12 -12 4 6 -2 Solution: x2 + 4x – 12 = (x + 6)(x - 2)

Examples continued 2. x2 - 9x + 20 -4 -5 20 -9 Solution: x2 - 9x + 20 = (x - 4)(x - 5)

You try… Factor: x2 – 6x + 5 Answer: (x – 1)(x – 5)

Extra Practice Factor 1. x2 + 6x + 5 (x + 5)(x + 1) 2. r2 – 12r + 35