Page 122 - Math Course 2 (Book 1)

Trinomials: ax + bx + c
2
Mo. 4

Lesson 2 Factor 24x – 22x + 3.
2
In this trinomial, a = 24, b = –22, and c = 3. Since b is
negative, m + n is negative. Since c is positive, mn is
KEY CONCEPTS: positive. So m and n must both be negative.
2
1. Factor trinomials of the form ax + bx + c.
2
2. Solve equations of the form ax + bx + c. Therefore, make a list of the negative factors of
24 • 3 or 72, and look for the pair of factors with the
sum of –22.

MO. 4 - L2a Factors of Sum of
72 Factors
Factoring Trinomials:
–1, –72 –73
ax + bx + c –2, –36 –38
2
–3, –24 –27
The correct factors
Let’s Begin –4, –18 –22 are –4 and –18.
2
2
24x – 22x + 3 = 24x + mx + nx + 3
Write the pattern.
Factor ax + bx + c = 24x – 4x –18x + 3 m = –4 and n = –18
2
2
2
Examples = (24x – 4x) + (–18x + 3) Group terms with
common factors.

2
Factor 5x + 27x + 10. = 4x(6x – 1) + (–3)(6x –1) Factor the GCF
from each grouping
In this trinomial, a = 5, b = 27, and c = 10. You need
to f nd two numbers with a sum of 27 and with a = (4x – 3)(6x – 1) Distributive Property
product of 5 • 10 or 50. Make an organized list of
the factors of 50 and look for the pair of factors
with the sum of 27. Answer (4x – 3)(6x – 1)

Factors of Sum of
50 Factors
2
Factor 4x + 24x + 32.
1, 50 51
2
The correct factors The GCF of the terms 4x , 24x, and 32 is 4. Factor
2, 25 27
are 2 and 25. this out f rst.
2
2
5x + 27x + 10 = 5x + mx + nx + 10 4x + 24x + 32 = 4(x + 6x + 8) Distributive
2
2
Write the pattern. Property
2
= 5x + 2x + 25x + 10 m = 2 and n = 25 Now factor x + 6x + 8. Since the lead coef cient is
2
1, f nd the two factors of 8 whose sum is 6.
2
= (5x + 2x) + (25x + 10) Group terms with
common factors. Sum of
Factors of 8
Factors
= x(5x + 2) + 5(5x + 2) Factor the GCF from 1, 8 9
each grouping. The correct factors
2, 4 6 are 2 and 4.
= (5x + 2)(x + 5) Distributive Property.
2
So, x + 6x + 4 = (x + 2)(x + 4).
Answer Thus, the complete factorization
Answer (5x + 2)(x + 5) 2
of 4x + 24x + 32 is 4(x + 2)(x + 4)

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