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There are 5 steps to factor a polynomial There are 5 steps to factor a polynomial Look for GCF There are 5 steps to factor a polynomial Look for GCF Look for a pattern There are 5 steps to factor a polynomial Look for GCF Look for a pattern Factor an easy trinomial There are 5 steps to factor a polynomial Look for GCF Look for a pattern Factor an easy trinomial Factor a hard trinomial There are 5 steps to factor a polynomial Look for GCF Look for a pattern Factor an easy trinomial Factor a hard trinomial Grouping We are going to talk about the third step There are 5 steps to factor a polynomial Look for GCF Look for a pattern Factor an easy trinomial Factor a hard trinomial Grouping Factoring easy trinomials is fairly simple. a trinomial Factoring easy trinomials is fairly simple. x2 - 4 x + 3 Factoring easy trinomials is fairly simple. The most important part is... x2 - 4 x + 3 Factoring easy trinomials is fairly simple. The most important part is... ...the last sign. x2 - 4 x + 3 last sign What is the most part of these trinomials? x2 - 10x - 20 - ? x2 - 4x + 3 + ? Identify the most important sign in these trinomials x2 + 3x - 5 Identify the most important sign in these trinomials x2 + 3x - 5 - x2 - 4x + 2 Identify the most important sign in these trinomials x2 - 4x -12 x2 + 3x - 5 - x2 - 4x + 2 + Identify the most important sign in these trinomials x2 - 4x -12 x2 + 3x - 5 - - x2 + 8x + 4 x2 - 4x + 2 + What is the most important sign in this trinomial? x2 +5x -6 + - This sign tells you two things... x2 - 4 x + 3 last sign This sign tells you two things... ...the signs of your factors, x2 - 4 x + 3 last sign This sign tells you two things... and whether you add or subtract the factors ...the signs of your factors, x2 - 4 x + 3 last sign For example... For example... x2 - 8x + 12 This polynomial has a '+' for its last sign For example... x2 - 8x + 12 a plus sign This polynomial has a '+' for its last sign so that means two things... For example... x2 - 8x + 12 This polynomial has a '+' for its last sign so that means two things... 1. the factor signs are the same For example... x2 - 8x + 12 This polynomial has a '+' for its last sign so that means two things... 2. the factors must be added 1. the factor signs are the same For example... x2 - 8x + 12 x2 - 3x - 12 factor signs are the same factor signs are different Answer each of the following If the factors must be added then the sign must be... x2 - 3x - 12 factor signs are different Answer each of the following x2 + 8x + 3 this sign is plus x2 - 8x + 12 this sign is plus so that means... x2 - 8x + 12 this sign is plus so that means... the factor signs will be the same x2 - 8x + 12 so the factors will either look like this this sign is plus so that means... the factor signs will be the same x2 - 8x + 12 so the factors will either look like this this sign is plus so that means... the factor signs will be the same x2 - 8x + 12 ( x + ) ( x + ) so the factors will either look like this this sign is plus so that means... the factor signs will be the same or this x2 - 8x + 12 ( x + ) ( x + ) ( x - ) ( x - ) Match the factor signs with the correct trinomial ( x - ) ( x - ) ? x2 - 5x + 2 ( x + ) ( x - ) ? x2 + 5x - 2 How do we tell which one it is? x2 - 8x + 12 the double positive? How do we tell which one it is? x2 - 8x + 12 the double positive? ( x + ) ( x + ) How do we tell which one it is? x2 - 8x + 12 the double positive ( x + ) ( x + ) How do we tell which one it is? x2 - 8x + 12 or the double negative? the double positive ( x + ) ( x + ) How do we tell which one it is? x2 - 8x + 12 or the double negative ( x - ) ( x - ) previous sign the double positive ( x + ) ( x + ) How do we tell which one it is? We can tell by the previous sign x2 - 8x + 12 or the double negative ( x - ) ( x - ) if that sign is positive the double positive ( x + ) ( x + ) How do we tell which one it is? We can tell by the previous sign x2 - 8x + 12 or the double negative ( x - ) ( x - ) then we use the double positive if that sign is positive the double positive ( x + ) ( x + ) How do we tell which one it is? We can tell by the previous sign x2 - 8x + 12 or the double negative ( x - ) ( x - ) then we use the double positive if that sign is positive the double positive ( x + ) ( x + ) How do we tell which one it is? We can tell by the previous sign x2 - 8x + 12 or the double negative but if that sign is negative ( x - ) ( x - ) then we use the double positive if that sign is positive the double positive ( x + ) ( x + ) How do we tell which one it is? We can tell by the previous sign x2 - 8x + 12 or the double negative but if that sign is negative ( x - ) ( x - ) double negative then use the ( x - ) ( x - ) ? Match the factor signs with the correct trinomial x2 - 4x + 5 ( x + ) ( x + ) ? x2 + 4x + 5 ( x - ) ( x + ) ? x2 - 4x - 5 ( x + ) ( x + ) So since the previous sign is negative negative x2 - 8x + 12 ( x - ) ( x - ) ( x + ) ( x + ) then we use the double negative factors So since the previous sign is negative negative x2 - 8x + 12 ( x - ) ( x - ) Find the correct signs for the factor (x - )(x + ) (x - )(x - ) (x + )(x + ) (x + )(x - ) x2 + 6x + 7 Find the correct signs for the factor (x - )(x + ) (x - )(x - ) (x + )(x + ) (x + )(x - ) x2 - 6x + 7 Find the correct signs for the factor (x - )(x + ) (x - )(x - ) (x + )(x + ) (x + )(x - ) x2 - 7x + 12 Find the correct signs for the factor (x - )(x + ) (x - )(x - ) (x + )(x + ) (x + )(x - ) x2 + 7x + 12 |