Factorin g by Grouping Your Name Date 1. Terms of an algebraic expression are separated by addition, which is indicated by a '+' or sign. The expression 6x2 + 3x - 12 has 3 terms. How many terms are there in each of the following expressions: 3) 6x342 Answer b) 6x2 + xy + y\" + 2 Answer c) 4x3y? - 13x3y?z + x3y?z Answer (1) 49(3))? + 9x2}! - x -y + xy Answer 2. Each term can have multiple factors (including a numerical coefficient). In 4x3y7z + 9x2yz - yz, the factors of the rst term are 4, x3, y?, 2 For ll-xzy3z + 6x2yz, what are the factors of the: a) 1\" term Answer b) 2"d term Answer 3. The Distributive Properly can be used to factor out common factors from each term of an expression. For example: ax2 + bx : x (ax + b) Factor: 4x3 + 12x2); - lxyZ Answer 4. The Greatest Common Factor (GCF) is the largest common factor that can be taken out of each term. To find the GCF: 24x\"y3z - 486222 + 36x23 - prime factor each term, 24x33: = 233x\"y32 express the factors using exponents 48x33: = 243x322: 36x7); = 223%! - for each factor/base that appears 223:8)! (z is not included in all the terms of the expression be cause there aren't use the smallest power of the base any 2's in the last term.) - simplify the factors. GCF = 12x2)! 5. The first step in factoring any expression is to factor out the GCF, if possible. 24x*y'z - 48x3yz + 36xy can be factored to: 12 x y(2x2y z - 4xyz + 3) Factor: 27x*y'z + 18xy z - 36x2y'z' + 54x y z' Answer_ 6. A common factor can also be a binomial. We can factor out the binomial in the same way we would factor out a single variable. Single variable: ax' + 7a = a (x2 + 7) Binomial: x2 ( x + 2) +7 (x + 2) = (x+ 2) (x2 + 7) Factor: a) 4x' (y - 2) - 3 (y - 2) Answer b) 6w(z - 5) + 3x(z - 5) - y(z - 5)