Chapter 9: Polynomials 9.5 Factoring Trinomials of the form ax 2 + bx + c (where a = 1) In lesson 9.4 we learned how to factor polynomials by pulling out the GCF. Today we will learn how to specifically factor trinomials when there is no GCF. Before we begin, consider the following polynomial expression: (x + 2)(x + 3) In lesson 9.2, we learned how to expand this polynomial by "FOIL"ing/distributing. When we FOIL it, we get this: (x + 2)(x + 3) = x 2 + 3x + 2x + 6 = x 2 + 5x + 6 Today, we will learn that factoring is the REVERSE process of FOILing. With factoring, we take an already expanded polynomial and write it as the product of two smaller factors.
Transcript
Chapter 9: Polynomials9.5 Factoring Trinomials
of the form ax2 + bx + c (where a = 1)
In lesson 9.4 we learned how to factor polynomials by pulling out the GCF. Today we will learn how to specifically factor trinomials when there is no GCF.
Before we begin, consider the following polynomial expression:
(x + 2)(x + 3)
In lesson 9.2, we learned how to expand this polynomial by "FOIL"ing/distributing. When we FOIL it, we get this:
(x + 2)(x + 3) = x2 + 3x + 2x + 6 = x2 + 5x + 6
Today, we will learn that factoring is the REVERSE processof FOILing. With factoring, we take an already expanded polynomial and write it as the product of two smaller factors.
Example 1:
Factor the previous example: x2 + 5x + 6
**Steps to Factoring Trinomials**1) Always first look for a GCF to factor out. If there is none, then:2) Multiply "a" and "c"3) Find 2 numbers that multiply to this number, and also add up to "b"4) Write your factored answer as (x + ___)(x + ___)5) Check your answer by FOILing. You should get the original problem back.
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Factoring Trinomials of the formax2 + bx + c (where a = 1)
Answer:
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Check:
Example 1: Factor x2 + 11x + 18
Example 2: Factor x2 + 7x + 10
Example 3: Factor x2 + 17x + 72
Example 5: Factor n2 6n + 8
Example 4: Factor x2 11x + 24
Example 6: Factor n2 14n + 45
Example 7: Factor x2 3x 18
Example 8: Factor x2 8x 20
Example 9: Factor x2 4x 12
Example 10: Factor x2 x 20
Example 13: Factor y2 + 2y 15
Example 11:Factor x2 + 7x 18
Example 12:Factor x2 + x 42
Example 14: Factor 6x2 + 66x + 60
Example 15: Factor 5y2 30y + 40
Example 16: Factor and find the "zeros" of the trinomial (Solve for x).
x2 + 3x = 18
Example 17: Factor and find the "zeros" of the function (Solve for x).
