This document discusses factoring trinomials of the form x^2 + bx + c. It explains that to factor such trinomials, you need to find two numbers whose sum is b and whose product is c. It then provides examples of factoring different types of trinomials, such as those where the two numbers have the same sign, different signs, or are not factorable. It emphasizes checking your factored results by multiplying them back out to verify they equal the original trinomial. Finally, it provides additional trinomials for the reader to practice factoring.

1. 15.2
Factoring Trinomials of the
Form x2 + bx + c

2. Factoring Trinomials
Recall by using the FOIL/Distribution 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 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
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).

4. 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
– 3, – 8 – 11
So x2 – 11x + 24 = (x – 3)(x – 8).

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

6. Prime Polynomials
Example
Factor the polynomial x2 – 6x + 10.
Since our two numbers must have a product of 10 and a
sum of – 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 prime
polynomial.

7. 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.

8. Factoring (You try some!)
Factor
9. x2 + 11x + 10
10. x2 – 17x + 60
11. x2 – 49
12. x2 – 12x + 36
(x + 10)(x + 1)
(x – 12)(x – 5)
(x – 7)(x + 7)
(x – 6)2