Do Now: Aim: How Do We Factor Trinomials? Multiply 1) (x+8)(x+4)

Factoring Simple Trinomials A simple trinomial is of the form ax2 + bx + c. The middle term of a simple trinomial is the sum of the last two terms of the binomials. The last term is the product of the last two terms of the binomials. The method used is the sum/product method. Look for two numbers that have a product equal to the last term and a sum equal to the numerical coefficient of the middle term.

Factoring Simple Trinomials 6a2 + 42a + 72 a2 + 9ab + 20b2 = 6(a2 + 7a + 12) = 6(a + 4)(a + 3) = (a + 4b)(a + 5b)

Factoring General Trinomials Factor: 3x2 + 17x + 10 Divide 1st term by the leading coefficient and multiply the last term by the leading coefficient Simplify Factor x2 + 17x + 30 and leave a space before each x ( x + 15)( x + 2) (3x + 15)(3x + 2) Put 3 back into each binomial Divide each binomial by the GCF if there is (are) (x + 5)(3x + 2)

Factor: 3x2 - 10x - 8 ( x – 12)( x + 2) (3x – 12)(3x + 2) Divide 1st term by the leading coefficient and multiply the last term by the leading coefficient Simplify Factor x2 + 17x + 30 and leave a space before each x ( x – 12)( x + 2) (3x – 12)(3x + 2) Put 3 back into each binomial Divide each binomial by the GCF if there is (are) (x – 4)(3x + 2)

(x + 6)(3x + 2) Factor the following trinomials 1. 6x2 + x – 15

Factor: 5(4 – 3x) + 8x(4 – 3x) =(4 – 3x)(5 + 8x)

Factoring Expressions With Complex Bases (a + 2)2 + 3(a + 2) + 2 Let A = (a + 2). A2 + 3A + 2 Replace (a + 2) with A. = (A + 2)(A + 1) Factor the trinomial. = [(a + 2) + 2] [(a + 2) + 1] Replace (a + 2) with A. = (a + 4)(a + 3) Simplify.

Factor by grouping Group into two binomials Factor by GFC if possible Factor completely

You Try It Factor each trinomial if possible. 1) x2 –10x + 24 7) x3 + 3x2 – x – 3