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Chapter 2

6. Chapter. Chapter 2. Factoring Polynomials. Factoring Trinomials of the Form x 2 + bx + c. Section. 6.2. Factoring Trinomials of the Form x 2 + bx + c. Objective. 1. Factoring Trinomials of the Form x 2 + bx + c. Recall by using the FOIL method that

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Chapter 2

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  1. 6 Chapter Chapter 2 Factoring Polynomials

  2. Factoring Trinomials of the Form x2 + bx + c Section 6.2

  3. Factoring Trinomials of the Form x2 + bx + c Objective 1

  4. Factoring Trinomials of the Form x2 + bx + c Recall by using the FOIL method that F O I L (x + 2)(x + 4) = x2 + 4x + 2x + 8 = x2 + 6x + 8

  5. Factoring Trinomials of the Form x2 + bx + c To factor x2 + bx + c into (x + one #)(x + another #), note that b is the sum of the two numbers and c is the product of the two numbers. So we’ll be looking for 2 numbers whose product is c and whose sum is b. Note: there are fewer choices for the product, so that’s why we start there first.

  6. Factoring Trinomials of the Form x2 + bx + c • To Factor a Trinomial of the Form x2 + bx + c The product of these numbers is c. x2 + bx + c = (x + )(x + ) The sum of these numbers is b.

  7. Example Factor the polynomial x2 + 13x + 30. • Since our two numbers must have a product of 30 and a sum of 13, the two numbers must both be positive. • Positive factors of 30 Sum of Factors • 1, 30 31 • 2, 15 17 • 3, 10 13 • Note, there are other factors, but once we find a pair that works, we do not have to continue searching. So x2 + 13x + 30 = (x + 3)(x + 10).

  8. Example Factor the polynomial x2 – 11x + 24. • Since our two numbers must have a product of 24 and a sum of –11, the two numbers must both be negative. • Negative factors of 24 Sum of Factors • –1, –24 –25 • –2, –12 –14 • –3, –8 –11 So x2 – 11x + 24 = (x – 3)(x – 8).

  9. Example Factor the polynomial x2 – 2x – 35. • Since our two numbers must have a product of –35 and a sum of – 2, the two numbers will have to have different signs. • Factors of –35 Sum of Factors • –1, 35 34 • 1, –35 –34 • –5, 7 2 • 5, –7 –2 So x2 – 2x – 35 = (x + 5)(x – 7).

  10. Example Factor: x2 – 6x + 10 • We look for two numbers whose product is 10 and whose sum is –6. The two numbers will have to both be negative. • Negative factors of 10 Sum of Factors • –1, –10 –11 • –2, –5 –7 Since there is not a factor pair whose sum is –6, x2 – 6x +10 is not factorable and we call it a primepolynomial.

  11. Check Your Result! • You should always check your factoring results by multiplying the factored polynomial to verify that it is equal to the original polynomial. • Many times you can detect computational errors or errors in the signs of your numbers by checking your results.

  12. Example Factor: x2 + 5xy + 6y2 • We look for two numbers whose product is 6y2 and whose sum is 5xy.

  13. Example Factor: x4 + 5x2 + 6 • We look for two factors of 6 whose sum is 5. • The numbers are 2 and 3.

  14. Factoring Out the Greatest Common Factor Objective 2

  15. Example Factor: • First factor out the greatest common factor, 3, from each term. • Now find two factors of ‒20 whose sum is ‒8.

  16. Example Factor:

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