EXAMPLE 1 Factor when b is negative and c is positive

Slides:

Advertisements

Similar presentations

Factoring Trinomials.

Advertisements

A f r i d i i m r a n S O L V IN G S Y ST E M S O F E Q U A T I O N S A f r i d i i m r a n

Factoring Trinomials When a 1.

Slide 1 Insert your own content. Slide 2 Insert your own content.

Chapter 1 The Study of Body Function Image PowerPoint

Quest ion 1? A.) answer B.) answer C.) correct answerD.) answer L C.) correct answer F.

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

Jeopardy Q 1 Q 6 Q 11 Q 16 Q 21 Q 2 Q 7 Q 12 Q 17 Q 22 Q 3 Q 8 Q 13

Title Subtitle.

Entry Task Solve for y 1) 2x + -3y < 12 2) x > ½ y - 7.

Multiplying monomials & binomials You will have 20 seconds to answer the following 15 questions. There will be a chime signaling when the questions change.

(x + 4)(x + 7) = x2 + 11x + 28 (x + 14)(x + 2) = x2 + 16x + 28

DIVIDING INTEGERS 1. IF THE SIGNS ARE THE SAME THE ANSWER IS POSITIVE 2. IF THE SIGNS ARE DIFFERENT THE ANSWER IS NEGATIVE.

MULT. INTEGERS 1. IF THE SIGNS ARE THE SAME THE ANSWER IS POSITIVE 2. IF THE SIGNS ARE DIFFERENT THE ANSWER IS NEGATIVE.

Teacher Name Class / Subject Date A:B: Write an answer here #1 Write your question Here C:D: Write an answer here.

Factoring Trinomials.

Factoring Trinomials.

Digital Lessons on Factoring

Objective The student will be able to:

4.6 Perform Operations with Complex Numbers

O X Click on Number next to person for a question.

5.9 + = 10 a)3.6 b)4.1 c)5.3 Question 1: Good Answer!! Well Done!! = 10 Question 1:

Adding Integers Absent Copy

Multiply/Divide integers Absent 10/14

AC Method of factoring ax2 + bx +c

The Greenebox Factoring Method

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

4.5 Solve Quadratic Equations by Finding Square Roots

FACTORING TRINOMIALS with leading coefficient

Factoring Trinomials.

Factoring ax2+bx +c ax2+bx +c

Addition 1’s to 20.

25 seconds left…...

Test B, 100 Subtraction Facts

What is Slope Assignment. List the four types of slope and sketch each type. 1.

11 = This is the fact family. You say: 8+3=11 and 3+8=11

EOC Practice #19 SPI

Use the substitution method

Bottoms Up Factoring. Start with the X-box 3-9 Product Sum

O X Click on Number next to person for a question.

X-box Factoring. X- Box 3-9 Product Sum Factor the x-box way Example: Factor 3x 2 -13x (3)(-10)= x 2x 3x 2 x-5 3x +2.

Solve an equation by multiplying by a reciprocal

EXAMPLE 3 Use synthetic division

Factoring a Quadratic Trinomial Step 2: Insert the two numbers that have a product of c and a sum of b. 2 and 5 are the factors of 10 that add up to 7.

Table of Contents Factoring - Perfect Square Trinomial A Perfect Square Trinomial is any trinomial that is the result of squaring a binomial. Binomial.

EXAMPLE 4 Use Descartes’ rule of signs Determine the possible numbers of positive real zeros, negative real zeros, and imaginary zeros for f (x) = x 6.

Objective: Learn to multiply and divide integers.

Standardized Test Practice

Multiplying Rational Numbers Essential Question: How do you multiply rational numbers? Unit 1-4.

6.3 Trinomial Squares Goals: To recognize a trinomial square and be able to factor it Remember to always factor out a common factor before you see if.

EXAMPLE 3 Use synthetic division Divide f (x)= 2x 3 + x 2 – 8x + 5 by x + 3 using synthetic division. – – 8 5 – 6 15 – 21 2 – 5 7 – 16 2x 3 + x 2.

Factoring Part 3. FACTORING #1: Take out the GCFEX: 2x 4 – 8x 3 + 4x 2 – 6x How to do it…. Find what is in common in each term and put in front. See what.

9.5 Factoring Trinomials. 9.5 – Factoring Trinomials Goals / “I can…”  Factor trinomials.

EXAMPLE 1 Multiply a monomial and a polynomial Find the product 2x 3 (x 3 + 3x 2 – 2x + 5). 2x 3 (x 3 + 3x 2 – 2x + 5) Write product. = 2x 3 (x 3 ) + 2x.

EXAMPLE 2 Finding a Mean Temperatures One of the coldest places on Earth is the Russian town of Verkhoyansk, located near the Arctic Circle. Find the mean.

Factoring Trinomials of the Form ax2 + bxy + cy2

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 +

Table of Contents Factoring – Signs in Trinomials When we factor trinomials into binomials, it is very important to understand the possible sign combinations.

Unit 8, Lesson 7a. (x+3)(x+2) Multiplying Binomials (FOIL) FOIL = x 2 + 2x + 3x + 6 = x 2 + 5x + 6.

INTEGERS – Product & Quotient. Multiplying Integers - remember our changing sign table ? + + changes to changes to changes to changes.

Factoring Quadratic Trinomials To Factor Trinomials in the Form x² + bx + c. OBJECTIVE C can be positive or negative.

HW: factoring trinomials WS. Factoring Trinomials Must be in STANDARD FORM Leading Coefficient MUST BE POSITIVE ONE! What MULTIPLIES to get the last term.

Which list of numbers is ordered from least to greatest? 10 –3, , 1, 10, , 1, 10, 10 2, 10 – , 10 –3, 1, 10, , 10 –3,

Example 2 Factor the polynomial. 12n n2 a. – 36 + = ( ) 2 n2 –

Presentation transcript:

EXAMPLE 1 Factor when b is negative and c is positive Factor 2x2 – 7x + 3. SOLUTION Because b is negative and c is positive, both factors of c must be negative. Make a table to organize your work. You must consider the order of the factors of 3, because the x-terms of the possible factorizations are different.

Factor when b is negative and c is positive EXAMPLE 1 Factor when b is negative and c is positive –x – 6x = –7x (x – 3)(2x – 1) 3, 1 1, 2 –3x – 2x = –5x (x – 1)(2x – 3) –1, –3 1,2 Middle term when multiplied Possible factorization Factors of 3 Factors of 2 Correct 2x2 – 7x + 3 = (x – 3)(2x – 1) ANSWER

EXAMPLE 2 Factor when b is positive and c is negative Factor 3n2 + 14n – 5. SOLUTION Because b is positive and c is negative, the factors of c have different signs.

Factor when b is negative and c is positive EXAMPLE 2 Factor when b is negative and c is positive n – 15n = –14n (n – 5)(3n + 1) –5, 1 1, 3 –n + 15n = 14n (n + 5)(3n – 1) 5, –1 5n – 3n = 2n (n – 1)(3n + 5) –1, 5 –5n + 3n = – 2n (n + 1)(3n – 5) 1, –5 Middle term when multiplied Possible factorization Factors of –5 Factors of 3 Correct 3n2 + 14n – 5 = (n + 5)(3n – 1) ANSWER

GUIDED PRACTICE for Examples 1 and 2 Factor the trinomial. 1. 3t2 + 8t + 4 (t + 2)(3t + 2) ANSWER 2. 4s2 – 9s + 5 (s – 1)(4s – 5) ANSWER 3. 2h2 + 13h – 7 (h + 7)(2h – 1) ANSWER