8-48-4factoring factoring axax - weber school...
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Holt Algebra 1
8-4 Factoring ax2 + bx + c8-4 Factoring ax2 + bx + c
Holt Algebra 1
Warm Up
Lesson Presentation
Lesson Quiz
Holt Algebra 1
8-4 Factoring ax2 + bx + c
Bell Quiz 8-4
Find each product.
1. (x – 2)(2x + 7)
2. (3y + 4)(2y + 9)
3. (3n – 5)(n – 7)
Factor each trinomial.
4. x2 +4x – 32
5. z2 + 15z + 36 10 pts
possible
2 pts
2 pts
2 pts
2 pts
2 pts
Holt Algebra 1
8-4 Factoring ax2 + bx + c
Questions on 8Questions on 8Questions on 8Questions on 8----3333
Holt Algebra 1
8-4 Factoring ax2 + bx + c
Factor quadratic trinomials of the form ax2 + bx + c.
Objective
Holt Algebra 1
8-4 Factoring ax2 + bx + c
In the previous lesson you factored trinomials of the form x2 + bx + c. Now you will factor trinomials of the form ax + bx + c, where a ≠ 0.
Holt Algebra 1
8-4 Factoring ax2 + bx + c
When you multiply (3x + 2)(2x + 5), the coefficient of the x2-term is the product of the coefficients of the x-terms. Also, the constant term in the trinomial is the product of the constants in the binomials.
(3x + 2)(2x + 5) = 6x2 + 19x + 10
Holt Algebra 1
8-4 Factoring ax2 + bx + c
To factor a trinomial like ax2 + bx + c into its binomial factors, write two sets of parentheses ( x + )( x + ).
Write two numbers that are factors of a next to the x’s and two numbers that are factors of c in the
other blanks. Multiply the binomials to see if you are correct.
(3x + 2)(2x + 5) = 6x2 + 19x + 10
Holt Algebra 1
8-4 Factoring ax2 + bx + c
Example 1: Factoring ax2 + bx + c by Guess and Check
Factor 6x2 + 11x + 4 by guess and check.
Write two sets of parentheses.
Try factors of 6 for the
coefficients and
factors of 4 for the
constant terms.
Holt Algebra 1
8-4 Factoring ax2 + bx + c
Steps to the “No Fuss” Factoring Method.1. Write 2 parentheses putting the first term of the
trinomial in both sets of parentheses.2. Multiply the 1st and last term and write it out to
the side.3. Find the factors.4. Select the two factors that the sum gives you
the middle term.5. Write the two factors in the parentheses.6. Factor out anything that can be factored out of
either parentheses and throw it away.7. Check your answer.
Holt Algebra 1
8-4 Factoring ax2 + bx + c
Example 2A: Factoring ax2 + bx + c When c is Positive
Factor each trinomial. Check your answer.
2x2 + 17x + 21
Holt Algebra 1
8-4 Factoring ax2 + bx + c
When b is negative and c is positive, the factors of c are both negative.
Remember!
Holt Algebra 1
8-4 Factoring ax2 + bx + c
Factor each trinomial. Check your answer.
3x2 – 16x + 16
Example 2B: Factoring ax2 + bx + c When c is Positive
Holt Algebra 1
8-4 Factoring ax2 + bx + cCheck It Out! Example 2
Factor each trinomial. Check your answer.
2a: 6x2 + 17x + 5 2b: 9x2 – 15x + 4
2c: 3x2 + 13x + 12
Holt Algebra 1
8-4 Factoring ax2 + bx + c
When c is negative, one factor of c will be positive and the other factor will be negative.
Holt Algebra 1
8-4 Factoring ax2 + bx + c
Example 3A: Factoring ax2 + bx + c When c is Negative
Factor each trinomial. Check your answer.
3n2 + 11n – 4
Holt Algebra 1
8-4 Factoring ax2 + bx + c
Factor each trinomial. Check your answer.
2x2 + 9x – 18
Example 3B: Factoring ax2 + bx + c When c is Negative
Holt Algebra 1
8-4 Factoring ax2 + bx + c
Factor each trinomial. Check your answer.
4x2 – 15x – 4
Example 3C: Factoring ax2 + bx + c When c is Negative
Holt Algebra 1
8-4 Factoring ax2 + bx + cCheck It Out! Example 3
Factor each trinomial. Check your answer.
3a: 6x2 + 7x – 3 3b: 4n2– n – 3
Holt Algebra 1
8-4 Factoring ax2 + bx + c
When the leading coefficient is negative, factor out –1 from each term before using
other factoring methods.
Holt Algebra 1
8-4 Factoring ax2 + bx + c
When you factor out –1 in an early step, you must carry it through the rest of the steps.
Caution
Holt Algebra 1
8-4 Factoring ax2 + bx + c
Example 4A: Factoring ax2 + bx + c When a is Negative
Factor each trinomial. Check your answer.
–2x2 – 5x – 3
Holt Algebra 1
8-4 Factoring ax2 + bx + cCheck It Out! Example 4
Factor each trinomial. Check your answer.
4a: –6x2– 17x – 12 4b: –3x2
– 17x – 10
Holt Algebra 1
8-4 Factoring ax2 + bx + c
�Section 8-4 (page 552) 1-6 all, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 49, 50, 64, 68, 90