Factoring Factor: Change an addition expression into a multiplication expression. 1. Always look for a common factor a. immediately take it out to the front of the expression, take out all common factors b. show what s left inside ONE set of parenthesis c. if you factor out the entire term, leave a 1 in its place 2x 2 10 8x 2 + 4x 3x 3 + 5x 2 + 7x a 2 b + a 4 b 2 3a 3 b
Factor: Change an addition expression into a multiplication expression. 1. Always look for a common factor a. immediately take it out to the front of the expression, take out all common factors b. show what s left inside ONE set of parenthesis 2. Identify the number of terms. If there was a common factor, then look at the number of terms Factor. 3. If there are only two terms, see if it is the difference squares a. a 2 b 2 = (a + b)(a b) w 2 16 y 3 9y 50v 2 2z 2 x 2 64
1. Always look for a common factor a. immediately take it out to the front of the expression, take out all common factors b. show what s left inside ONE set of parenthesis 2. Identify the number of terms. If there was a common factor, then look at the number of terms 3. If there are four terms: a. first try splitting the expression into two parts, right down the middle i. factor out what s common to the first two terms ii. factor out what s common to the second two terms iii. if what s left in the parenthesis is the same, write down that factor iv. show what s left in a new set of parentheses. b. Move the first term to the end then split the expression down the middle i. factor out what s common to the first two terms ii. factor out what s common to the second two terms iii. if what s left in the parenthesis is the same, write down that factor iv. show what s left in a new set of parentheses. ax 3x + 2a 6 x 2 y 2 + 10y 25 2x + 4y 3x 2 6xy c 3 c 2 u 25c + 25u
If subtraction is written backwards, factor out a negative. When you factor out the negative sign, you write the subtraction switched around. Beware of backwards subtraction. C(x y) + (y x) d(3 x) f(x 3) C(x y) (x y): not factored, still subtraction d(3 x) + f(3 x) (x y)(c 1) (3 x)(d + f) y(x 3) (3 x) 7x(y 1) + 4(1 y) 4x + 6y 2ax 3ay xw yw 5x + 5y
1. Always look for a common factor b. immediately take it out to the front of the expression, take out all common factors c. show what s left inside ONE set of parenthesis 2. Identify the number of terms. If there was a common factor, then look at the number of terms 3. If there are three terms, and the leading coefficient is positive: Trial and Error Method a. find all the factors of the first term b. find all the factors of the last term c. Within 2 sets of parentheses, i. place the factors from the first term in the front of the parentheses ii. place the factors from the last term in the back of the parentheses d. NEVER put common factors together in one parenthesis. e. check the last sign, i. if the sign is plus: use the SAME signs, the 1 in front of the 2 nd term ii. if the sign is minus: use different signs, one plus and one minus f. smile to make sure you get the middle term i. multiply the inner most terms together ii. multiply the outer most terms together iii. add the two products together. 6x 2 13x + 6 8x 2 + 10x 25 2d 2 + 13d + 20 10x 2 24x 18
4. Always look for a common factor d. immediately take it out to the front of the expression, take out all common factors e. show what s left inside ONE set of parenthesis 5. Identify the number of terms. If there was a common factor, then look at the number of terms 6. If there are three terms, and the leading coefficient is positive: AC Method a. Multiply the first term to the last term (make sure you have descending order) b. find all the factors of the produce c. find the two factors that add to the middle term d. now rewrite the expression replacing the middle term with the two factors e. factor by grouping: first two term and then the last two terms 2t 2 + 5t 12 2yz 3 + 17yz 2 + 8yz 4x 2 + 6x + 2 16x 2 16x 12
7x 3 14x 2 6x 2 y + 3xy 9xy 2 24p 3 + 33p 2 8p 11 5z 2 45w 2 15t 2 20t 50 2x 4 y 3 5x 3 y 3 18x 2 y 3
Factor: Change an addition expression into a multiplication expression. 1. Always look for a common factor a. immediately take it out to the front of the expression, take out all common factors b. show what s left inside ONE set of parenthesis 2. Identify the number of terms. If there was a common factor, then look at the number of terms 3. If there are only two terms, see if it is the sum or difference of perfect cubes a. a 3 b 3 = (a b)(a 2 + ab + b 2 ) b. a 3 + b 3 = (a + b)(a 2 ab + b 2 ) w 3 27 y 3 + 8 250 + 2z 3 x 3 64w 3