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4.2

Factoring Trinomials of the Form x 2 + bx + c. 4.2. Factoring Trinomials of the Form x 2 + bx + c. Recall by using the FOIL method that F O I L ( x + 2)( x + 4) = x 2 + 4 x + 2 x + 8

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4.2

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  1. Factoring Trinomials of the Form x2 + bx + c 4.2

  2. 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 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.

  3. 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.

  4. 3, 10 13 Factoring Polynomials 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 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).

  5. – 3, – 8 – 11 Factoring Polynomials 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 So x2 – 11x + 24 = (x – 3)(x – 8).

  6. 5, – 7 – 2 Factoring Polynomials 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 So x2 – 2x – 35 = (x + 5)(x – 7).

  7. Prime Polynomials 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.

  8. 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.

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