Factoring Trinomials with a > 1 Factor trinomials when the coefficient of x 2 is a number greater than 1. ax 2 + bx + c.

Slides:

Advertisements

Similar presentations

Factor these on your own looking for a GCF. Try these on your own:

Advertisements

Factoring Trinomials When a=1 ALWAYS check for GCF first! Factor trinomials in the standard form ax²+ bx + c Solve equations in the standard form ax²+

AC Method of factoring ax2 + bx +c

2.6 Factor x2 + bx + c.

Factoring x2 + bx + c Warm Up Lesson Presentation Lesson Quiz.

8-4 Factoring ax 2 + bx + c Warm Up Warm Up Lesson Presentation Lesson Presentation California Standards California StandardsPreview.

Warm-ups Find each product. 1. (x – 2)(2x + 7) 2. (3y + 4)(2y + 9) 3. (3n – 5)(n – 7) Factor each trinomial. 4. x 2 +4x – z z + 36.

7-4 Factoring ax2 + bx + c Warm Up Lesson Presentation Lesson Quiz

7-3 Factoring x2 + bx + c Warm Up Lesson Presentation Lesson Quiz

Objective Factor quadratic trinomials of the form x2 + bx + c.

7-3 Factoring x2 + bx + c Warm Up Lesson Presentation Lesson Quiz

Factoring Trinomials of the form x 2 + bx + c Chapter 5.3.

To factor a trinomial of the form: x2 + bx + c

7-3 Factoring x2 + bx + c Warm Up Lesson Presentation Lesson Quiz

Apply basic factoring techniques to second degree polynomials

8-4 Factoring ax2 + bx + c Warm Up Lesson Presentation Lesson Quiz

Table of Contents Factoring: Trinomial (ax 2 + bx + c) Example: Factor 6x x - 2. Second, find two numbers whose product is ac and whose sum is b.

Factoring Trinomials. Recall by using the FOIL method that F O I L (x + 2)(x + 4) = x 2 + 4x + 2x + 8 = x 2 + 6x + 8 To factor x 2 + bx + c into (x +

Preview Warm Up California Standards Lesson Presentation.

Chapter 7 Section 3 and 4 Factoring. Objectives  Factor quadratic trinomials of the form x 2 + bx + c. Factor quadratic trinomials of the form ax 2 +

Factoring Trinomials of the Form ax 2 + bx + c, where a  Factor trinomials of the form ax 2 + bx + c, where a  1, by trial. 2.Factor trinomials.

Objective The student will be able to: factor trinomials of the type ax 2 + bx + c with grouping. Designed by Skip Tyler, Varina High School.

2.4 part 1 - Basic Factoring I can... - Factor using GCF -Factor a difference of two perfect squares -Factor basic trinomials.

Holt McDougal Algebra 1 Factoring x 2 + bx + c Holt Algebra 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz Holt McDougal.

Factoring – Day 4 Factoring Trinomials Objective: To factor trinomials whose quadratic coefficient is 1.

Holt McDougal Algebra 1 Factoring x 2 + bx + c Factor quadratic trinomials of the form x 2 + bx + c. Objective.

Factoring a polynomial means expressing it as a product of other polynomials.

Holt McDougal Algebra Factoring x 2 + bx + c Factor quadratic trinomials of the form x 2 + bx + c. Objective multiply two binomials using the Distributive.

Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Section 6.3 Factoring Trinomials of the form x 2 + bx + c.

Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Chapter 5 Polynomials and Factoring.

MTH Algebra Factoring Trinomials of the form ax 2 + bx + c where a = 1 Chapter 5 Section 3.

7-3 Factoring x2 + bx + c Warm Up Lesson Presentation Lesson Quiz

Multiply (x+3)(2x-7) Factor 3. 42x – 7

Warm-up: Factor Completely

Section R.4 Factoring.

7-4 Factoring ax2 + bx + c Warm Up Lesson Presentation Lesson Quiz

Factoring ax2 + bx + c Warm Up Lesson Presentation Lesson Quiz

Lesson 7.6 EQ: How do you factor a polynomial when leading coefficient is not 1? Topic/Objective: To factor trinomials in the form ax2 +bx + c Factor.

7-4 Factoring ax2 + bx + c Warm Up Lesson Presentation Lesson Quiz

Factoring ax2 + bx + c Warm Up Lesson Presentation Lesson Quiz

8-4 Factoring ax2 + bx + c Warm Up Lesson Presentation Lesson Quiz

8-3 Factoring x2 + bx + c Warm Up Lesson Presentation Lesson Quiz

7-3 Factoring x2 + bx + c Warm Up Lesson Presentation Lesson Quiz

Factor into pairs like in “T” Find the pair whose sum is “b”

8-3 Factoring x2 + bx + c Warm Up Lesson Presentation Lesson Quiz

Objective Factor quadratic trinomials of the form ax2 + bx + c.

Factor into pairs like in “T” Find the pair whose sum is “b”

Factoring x2 + bx + c Warm Up Lesson Presentation Lesson Quiz

Factoring ax2 + bx + c Warm Up Lesson Presentation Lesson Quiz

7-4 Factoring ax2 + bx + c Warm Up Lesson Presentation Lesson Quiz

7-3 Factoring x2 + bx + c Warm Up Lesson Presentation Lesson Quiz

Example 1A: Factoring Trinomials by Guess and Check

Factoring ax2 + bx + c Warm Up Lesson Presentation Lesson Quiz

Factoring ax2 + bx + c Warm Up Lesson Presentation Lesson Quiz

Factoring ax2 + bx + c Warm Up Lesson Presentation Lesson Quiz

Factoring Trinomials Day #1

Factoring Trinomials with Last Term POSITIVE Guess & Check Method

Warm-up: Factor Completely

7-4 Factoring ax2 + bx + c Warm Up Lesson Presentation Lesson Quiz

7-4 Factoring ax2 + bx + c Warm Up Lesson Presentation Lesson Quiz

8-4 Factoring ax2 + bx + c Warm Up Lesson Presentation Lesson Quiz

7-3 Factoring x2 + bx + c Warm Up Lesson Presentation Lesson Quiz

7-4 Factoring ax2 + bx + c Warm Up Lesson Presentation Lesson Quiz

There is a pattern for factoring trinomials of this form, when c

Factoring Trinomials.

Warm-up: Factor Completely

Warm-up: Factor Completely

Presentation transcript:

Factoring Trinomials with a > 1 Factor trinomials when the coefficient of x 2 is a number greater than 1. ax 2 + bx + c

3x x Multiply 3 times 6. product sum To make the sum positive, both numbers must be positive. Use the coefficient of x 2 in both parentheses: ( 3x ) ( 3x ) Fill in the numbers… ( 3x + 2 ) ( 3x + 9 ) Factor any common terms from each parenthesis. ( 3x + 2 ) ( 3x + 9 ) 1 3 ( 3x + 2 ) ( x + 3 ) Check using the F.O.I.L. method: ( 3x + 2 ) ( x + 3 ) 3x 2 + 9x + 2x + 6 3x x + 6

3x 2 + 7x – 6 – –1 18 –2 9 Multiply 3 times – 6. product sum To make the sum positive, the largest number must be positive. Use the coefficient of x 2 in both parentheses: ( 3x ) ( 3x ) Fill in the numbers… ( 3x – 2 ) ( 3x + 9 ) Factor any common terms from each parenthesis. ( 3x – 2 ) ( 3x + 9 ) 1 3 ( 3x – 2 ) ( x + 3 ) Check using the F.O.I.L. method: ( 3x – 2 ) ( x + 3 ) 3x 2 + 9x – 2x – 6 3x 2 + 7x – 6

3x 2 – 7x – 6 –18 – 7 1 –18 2 – 9 Multiply 3 times – 6. product sum To make the sum negative, the largest number must be negative. Use the coefficient of x 2 in both parentheses: ( 3x ) ( 3x ) Fill in the numbers… ( 3x + 2 ) ( 3x – 9 ) Factor any common terms from each parenthesis. ( 3x + 2 ) ( 3x – 9 ) 1 3 ( 3x + 2 ) ( x – 3 ) – 17 – 7 Check using the F.O.I.L. method: ( 3x + 2 ) ( x – 3 ) 3x 2 – 9x + 2x – 6 3x 2 – 7x – 6

9x 2 – 12x – 12 –1 –36 –2 –18 –3 –12 –4 –9 –6 Multiply 9 times 4. product sum To make the sum negative, both numbers must be negative. Use the coefficient of x 2 in both parentheses: ( 9x ) ( 9x ) Fill in the numbers… ( 9x – 6 ) ( 9x – 6 ) Factor any common terms from each parenthesis. ( 9x – 6 ) ( 9x – 6 ) 3 ( 3x – 2 ) – 37 – 20 Check using the F.O.I.L. method: ( 3x – 2 ) 9x 2 – 6x – 6x + 4 9x 2 – 12x + 4 – 15 – 13 – 12 ( 3x – 2 ) 2

4x 2 – 9 – – 36 6 – 6 Multiply – 9 times 4. product sum To make the sum zero, both numbers must be the same but opposite signs. Use the coefficient of x 2 in both parentheses: ( 4x ) ( 4x ) Fill in the numbers… ( 4x + 6 ) ( 4x – 6 ) Factor any common terms from each parenthesis. ( 4x + 6 ) ( 4x – 6 ) 2 ( 2x + 3 ) ( 2x – 3 ) – 35 0 Check using the F.O.I.L. method: ( 2x + 3 ) ( 2x – 3 ) 4x 2 – 6x + 6x – 9 4x 2 – 9

ALWAYS check your work when factoring trinomials by using the FOIL method.