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Factoring Trinomials

Factoring Trinomials. Using Tic-Tac-Toe (x + a)(x + b). Tic-tac-toe is like putting together a puzzle….. Don’t get frustrated… If some factors don’t work… Just keep trying… When trying factors…go in numerical order…. ax 2 + bx + c ax 2 - bx + c. ax 2 + bx – c ax 2 - bx - c.

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Factoring Trinomials

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  1. Factoring Trinomials Using Tic-Tac-Toe (x + a)(x + b)

  2. Tic-tac-toe is like putting together a puzzle….. • Don’t get frustrated… • If some factors don’t work… Just keep trying… • When trying factors…go in numerical order…

  3. ax2 + bx + c ax2 - bx + c ax2 + bx – c ax2 - bx - c SIGNS!! Negative “c” Positive “c” LOOK HERE FIRST!!! Add factors Same Signs Both will Be positive LOOK HERE FIRST!!! Subtract factors Opposite Signs Larger # will Be positive LOOK HERE FIRST!!! Add factors Same Signs Both will Be Negative Larger # will Be Negative LOOK HERE FIRST!!! Subtractfactors Opposite Signs

  4. Remember to check for GCF first!! NO GCF? factors 0f 144 that will go into 3rd column terms (1)(144) no (12)(12) = yes This sign tells you to add The factors. Same Signs (-1)(-144) ? -24 No (-2)(-72) ? -24 No (-3)(-48) ? -24 No (-4)(-36) ? -24 No (-6)(-24) ? -24 No (-12)(-12) ? -24 Yes!! Factors which will ADD to give -24 This signs shows Both signs Will be neg • Place first term in first spot • Place last term in next spot • Multiply these two • Determine the signs • Now factor down column 3. List all the factors and choose the ones that will add/subtract to give you the middle term. • Next, factor the middle column down. • Last, factor the first column down. • Check yourself, multiply ACROSS (L to R) all rows and UP all columns to see if you get the correct products.

  5. Remember to check for GCF first!! NO GCF? factors 0f 21 that will go into 3rd column terms (1)(21) no (3)(7) = yes This sign tells you to add The factors. Same Signs This signs shows Both signs Will be neg (-1)(-21) ? -10 No (-3)(-7) ? -10 Yes!! Factors which will ADD to give -10 • Place first term in first spot • Place last term in next spot • Multiply these two • Determine the signs • Now factor down column 3. List all the factors and choose the ones that will add/subtract to give you the middle term. • Next, factor the middle column down. • Last, factor the first column down. • Check yourself, multiply ACROSS (L to R) all rows and UP all columns to see if you get the correct products.

  6. Remember to check for GCF first!! NO GCF? factors 0f 10 that will go into 3rd column terms (1)(10) no (2)(5) = yes This sign tells you to add The factors. Same Signs This signs shows Both signs Will be pos (1)(10) ? 7 No (2)(5) ? 7 Yes!! Factors which will ADD to give 7 • Place first term in first spot • Place last term in next spot • Multiply these two • Determine the signs • Now factor down column 3. List all the factors and choose the ones that will add/subtract to give you the middle term. • Next, factor the middle column down. • Last, factor the first column down. • Check yourself, multiply ACROSS (L to R) all rows and UP all columns to see if you get the correct products.

  7. Remember to check for GCF first!! NO GCF? factors 0f 30 that will go into 3rd column terms (1)(30) no (5)(6) = yes This sign tells you to add The factors. Same Signs This signs shows Both signs Will be pos (1)(30) ? 11 No (2)(15) ? 11 no (3)(10) ? 11 no (5)(6) ? 11 yes !!! Factors which will ADD to give 11 • Place first term in first spot • Place last term in next spot • Multiply these two • Determine the signs • Now factor down column 3. List all the factors and choose the ones that will add/subtract to give you the middle term. • Next, factor the middle column down. • Last, factor the first column down. • Check yourself, multiply ACROSS (L to R) all rows and UP all columns to see if you get the correct products.

  8. Remember to check for GCF first!! NO GCF? factors 0f -8 that will go into 3rd column terms (1)(8) yes This sign tells you to sub The factors. Opp. Signs This signs shows the sign Of the larger # (1)(-8) ? -7 Yes Factors which will subtract to give -7 • Place first term in first spot • Place last term in next spot • Multiply these two • Determine the signs • Now factor down column 3. List all the factors and choose the ones that will add/subtract to give you the middle term. • Next, factor the middle column down. • Last, factor the first column down. • Check yourself, multiply ACROSS (L to R) all rows and UP all columns to see if you get the correct products.

  9. NO GCF? factors 0f -24 that will go into 3rd column terms (4)(-6) yes This signs shows the sign Of the larger # This sign tells you to sub The factors. Opp. Signs Factors which will subtract to give -2 (1)(-24) ? -2 no (2)(-12) ? No (3)(-8) ? No (4)(-6) ? yes • Place first term in first spot • Place last term in next spot • Multiply these two • Determine the signs • Now factor down column 3. List all the factors and choose the ones that will add/subtract to give you the middle term. • Next, factor the middle column down. • Last, factor the first column down. • Check yourself, multiply ACROSS (L to R) all rows and UP all columns to see if you get the correct products.

  10. Now let’s solve these quadratics. The root (solution) is 12 The roots (solutions) are 3 and 7

  11. The roots are -5 and -2 The roots are -5 and -6 The roots are -1 and 8 The roots are -4 and 6

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