Download Section 6.2

Factoring Trinomials With Leading Coefficient of "1" - Section 6.2
We want to factor polynomials of the form x 2 + bx + c where b and c are real numbers.
Consider the following products:
x + 4x + 3 = x 2 + 3x + 4x + 12 = x 2 + 7x + 12
x − 4x − 3 = x 2 − 3x − 4x + 12 = x 2 − 7x + 12
x + 4x − 3 = x 2 − 3x + 4x − 12 = x 2 + x − 12
How to factor trinomials of the form x 2 + bx + c
1. Enter x as first term of each factor
x 2 + bx + c = x +
x +

2. List all the pairs of factors of c.
3. Select the pair of these factors that add to b. Call these two factors m and n and factor the trinomial as
x 2 + bx + c = x + mx + n
4. Check by multiplying!
If there are no factors of c that add to b, the polynomial cannot be factored and is called "prime"
Help with finding m and n :
● If c is positive, m and n have the same sign. In this case, if b is positive, so are m and n. If b is negative, then so
are m and n.
● If c is negative, m and n have the opposite sign. In this case, if b is positive, the absolute value of the positive
one of m and n is larger than the absolute value of the negative one. If b is negative, the absolute value of the
negative one of m and n is larger than the absolute value of the positive one.
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Examples: Factor the trinomial as a product of two binomials
1. x 2 + 5x + 6
2. z 2 − 2z − 35
3. a 2 − 15a + 54
4. x 2 + 4x − 10
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Factoring a trinomial in two variables:
5. x 2 − 4xy + 3y 2
6. x 2 + 13xy − 14y 2
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Completely Factoring Polynomials:
Always start with the GCF. Then try and use other techniques to completely factor the polynomial.
7. 2x 3 + 6x 2 − 56x
8. −2t 2 − 10t + 28
9. 20x 2 y − 100xy + 120y
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