2. Chapter 7
Factoring

3. 7.2
Factoring Trinomials

4. Factor trinomials when the coefficient of the squared term is 1.
7.2 Factoring Trinomials
Objectives
Factor trinomials when the coefficient of the squared term is 1.
Factor trinomials when the coefficient of the squared term is not 1.
Use an alternative method of factoring trinomials.
Factor by substitution.
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5. Factor Out the Greatest Common Factor
7.2 Factor Trinomials
Factor Out the Greatest Common Factor
The product of two binomials sometimes gives a trinomial. For example:
So, we have two processes that “undo” each other.
Multiplying
Factored form
Product
Factoring
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6. 7.2 Factor Trinomials
Factoring Trinomials When the Coefficient of the Squared Term is 1
Multiplying binomials uses the FOIL method, and factoring involves using the FOIL method backwards.
Product of x and x is x2. F L
Product of 5 and – is –35.
Sum of the product of outer and inner terms O I
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7. 7.2 Factor Trinomials Factoring Trinomials When the Coefficient
of the Squared Term is 1
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8. Factoring Trinomials in Form
7.2 Factor Trinomials
Factoring Trinomials in Form
Step 1
Step 2
Coefficient of middle term
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9. Factoring Trinomials in Form
7.2 Factor Trinomials
Factoring Trinomials in Form
The required numbers are –8 and 4, so
You should always check your answer by multiplying the factors to see if you get the original polynomial.
Guidelines for Factoring Trinomials
If the last term is positive, the factors will have the form
( ___ + ___ ) ( ___ + ___ ) or ( ___ – ___ ) ( ___ – ___ )
The + or – sign is determined by the coefficient of the middle term.
If the last term is negative, the factors will have the form
( ___ + ___ ) ( ___ – ___ ) or ( ___ – ___ ) ( ___ + ___ )
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10. Factoring a Trinomial With A Common Factor
7.2 Factor Trinomials
Factoring a Trinomial With A Common Factor
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11. 7.2 Factor Trinomials Factoring Trinomials When the Coefficient
of the Squared Term is Not 1
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12. Solution 7.2 Factor Trinomials
Factoring Trinomials When the Coefficient
of the Squared Term is Not 1
Solution
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13. 7.2 Factor Trinomials
Factoring Trinomials When the Coefficient
of the Squared Term is Not 1
Listing all the pairs of numbers whose product is –24 to find a pair whose sum is –10, only 2 and –12 have a sum of –10.
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14. 7.2 Factor Trinomials Factoring Trinomials When the Coefficient
of the Squared Term is Not 1
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15. Factoring Other Trinomials by Trial and Error
7.2 Factor Trinomials
Factoring Trinomials When the Coefficient
of the Squared Term is Not 1
Factoring Other Trinomials by Trial and Error
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16. Factoring Other Trinomials by Trial and Error
7.2 Factor Trinomials
Factoring Trinomials When the Coefficient
of the Squared Term is Not 1
Factoring Other Trinomials by Trial and Error
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17. Factoring Other Trinomials by Trial and Error
7.2 Factor Trinomials
Factoring Trinomials When the Coefficient
of the Squared Term is Not 1
Factoring Other Trinomials by Trial and Error
Here are the possibilities, each of which produces the correct first and last term, 3x2 and –2, respectively.
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18. Trial and Error (Alternative Method) Summarized
7.2 Factor Trinomials
Factoring Trinomials When the Coefficient
of the Squared Term is Not 1
Trial and Error (Alternative Method) Summarized
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19. 7.2 Factor Trinomials
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20. Factoring a Polynomial Using Substitution
7.2 Factor Trinomials
Factoring a Polynomial Using Substitution
Sometimes we can factor more complicated problems by substituting a variable for an expression.
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21. Factoring a Polynomial Using Substitution
7.2 Factor Trinomials
Factoring a Polynomial Using Substitution
CAUTION
Remember to make the final substitution of (x – 2) for y.
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22. 7.2 Factor Trinomials
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