Page 133 - Math Course 2 (Book 1)

Factoring: Trinomials

Mo. 4

Lesson 4 b is Negative and c is Positive

Example

KEY CONCEPTS:
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2
1. Factor trinomials of the form x + bx + c. Factor x – 12x + 27.
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2. Solve equations of the form x + bx + c.
In this trinomial, b = –12 and c = 27. This means
m + n is negative and mn is positive. So m and n
must both be negative. Make a list of the negative
MO. 4 - L4a factors of 27, and look for the pair with a sum of
–12.
Trinomials: x + bx + c Factors of 27 Sum of Factors
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–1, –27 –28 The correct
factors are
–3, –9 –12 –3 and –9.
Key Concept
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x – 12x + 27 = (x + m)(x + n) Write the pattern.
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Factoring x + bx + c = (x – 3)(x – 9) m = –3 and n = –9
Answer (x – 3)(x – 9)
Words To factor quadratic trinomials of the
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form x + bx + c, f nd two integers, m
and n, with a sum equal to b and with a Check
You can check this result by using a graphing
product equal to c. calculator. Graph y = x – 12x + 27 and y = (x – 3)
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Then write x + bx + c using the pattern (x – 9) on the same screen. Since only one graph
(x + m)(x + n) appears, the two graphs must coincide. Therefore,
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Symbols x + bx + c = (x + m)(x + n) when the trinomial has been factored correctly.
m + n = b and mn = c.
2
Example x + 5x + 6 = (x + 2)(x + 3), since
2 + 3 = 5 and 2 • 3 = 6.

Let’s Begin

b and c are Positive

Example

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2
Factor x + 7x + 12. x + 7x + 12 = (x + m)(x + n) Write the pattern.
In this trinomial, b = 7 and c = 12. You need to f nd = (x + 3)(x + 4) m = 3 and n = 4.
two numbers with a sum of 7 and a product of 12.
Make an organized list of the factors of 12, and Answer (x + 3)(x + 4)
look for the pair of factors with a sum of 7.
Check
Factors of 12 Sum of Factors You can check the result by multiplying the two
1, 12 13 factors.
The correct F O I L
2, 6 8 factors are (x + 3)(x + 4) = x + 4x + 3x + 12 FOIL method
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3, 4 7 3 and 4. = x + 7x + 12 Simplify.
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