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Algebra 2

Algebra 2. 7.2: Factoring Trinomials (Reverse FOIL). Factoring x 2 + bx + c Leading coefficient is 1!!!. 1. ( ) with a variable in each group: (x )(x ) 2. Draw a big X. The third term goes on top the middle # goes on bottom.

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Algebra 2

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  1. Algebra 2 7.2: Factoring Trinomials (Reverse FOIL)

  2. Factoring x2 + bx + cLeading coefficient is 1!!! 1. ( ) with a variable in each group: (x )(x ) 2. Draw a big X. The third term goes on top the middle # goes on bottom. 3. Think of two #’s that multiply to get the top, but the same #’s add to get the bottom. - Hint!!! List the factors of the top # if you get stuck. 4. Place the two correct numbers and their signs in the ( )’s. It doesn’t matter which number goes where!!!

  3. Factoring x2 + bx + c 1) 2) 3) 4) ( )( ) ( )( ) + 6 r + - 4 a - r 2 a 2 ( )( ) ( )( ) - 5 y + - 5c b + y 7 b 2c

  4. Factoring ax2 + bx + cLeading coefficient is not 1!!! 1. Make bracket, then multiply 1st and 3rd terms. 2. Draw big X. # on bracket goes on top the middle # goes on bottom. 3. Think of two #’s that multiply to get the top, but the same #’s add to get the bottom. - Hint!!! List the factors of the top # if you get stuck. 4. Make a box, then divide into 4 smaller boxes. 5. Place 1st term in upper left and 3rd term in lower right from the trinomial. Place #’s from Step 3 into other boxes, then put an x next to them. 6. Find GCF of top and bottom boxes Find GCF of boxes on left & boxes on right *The answer will be right in front of your face!!!*

  5. Factoring ax2 + bx + c 1) 2) 12×-2=-24: You want two numbers that multiply to give you -24 and add to give you -5: They are -8 and 3: 3×2=6: You want two numbers that multiply to give you 6 and add to give you 7: They are 1 and 6: 1 1 4x 3x 3x x -2 2

  6. Factoring out the GCF 1st!!! 1) GCF = 2) GCF = 3×-12=-36: You want two numbers that multiply to give you -36 and add to give you -16: They are -18 and 2: 2×-2=-4: You want two numbers that multiply to give you -4 and add to give you 3: They are -1 and 4: -6 -1 x 2y y 3x 2 2

  7. Factoring ax4 + bx2 + c 1) 2) 6×-20=-120: You want two numbers that multiply to give you -120 and add to give you 7: They are 15 and -8: -4 3y2 2y2 5

  8. Helpful Hint: These can be in either order

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