FACTORING SPECIAL CASES. The vocabulary of perfect squares Perfect squares are numbers like 4, 9, 16, 25, etc. Any variable to an even power is a perfect.

Slides:

Advertisements

Similar presentations

Factoring – Sum and Difference of Two Cubes

Advertisements

Factoring trinomials ax² + bx +c a = any number besides 1 and 0

RULES FOR FACTORING Step 1: CMF Step 2: Binomial? DOTS?

(2.8) Factoring Special Products OBJECTIVE: To Factor Perfect Square Trinomials and Differences of Squares.

Factoring Decision Tree

Bellringer part two Simplify (m – 4) 2. (5n + 3) 2.

Special Products of Polynomials.

Chapter 9 Polynomials and Factoring A monomial is an expression that contains numbers and/or variables joined by multiplication (no addition or subtraction.

Perfect Squares and Factoring

9.1 Adding and Subtracting Polynomials

For Common Assessment Chapter 10 Review

Greatest Common Factor The Greatest Common Factor is the largest number that will divide into a group of numbers Examples: 1.6, , 55 GCF = 3 GCF.

Chapter 8: Factoring.

Factoring Review Review Tying it All Together Shortcut for the Shortcuts.

Special Cases of Factoring Chapter 5.5 Perfect Square Trinomials a 2 + 2ab + b 2 (a + b) 2 = a 2 – 2ab + b 2 (a – b) 2 =

Factoring Perfect Square Trinomials

Algebra 10.3 Special Products of Polynomials. Multiply. We can find a shortcut. (x + y) (x – y) x² - xy + - y2y2 = x² - y 2 Shortcut: Square the first.

2.3 Factor and Solve Polynomial Expressions Pg. 76.

Factoring Differences of Squares. Remember, when factoring, we always remove the GCF (Greatest Common Factor) first. Difference of Squares has two terms.

Factoring Review Greatest Common Factor, Difference of Squares, Box Method, Quadratic Formula.

To factor means to write a number or expression as a product of primes. In other words, to write a number or expression as things being multiplied together.

Factor Perfect Squares and Factoring Algebra 1 Glencoe McGraw-HillLinda Stamper.

Factor the following special cases

WARM UP SOLVE USING THE QUADRATIC EQUATION, WHAT IS THE EXACT ANSWER. DON’T ROUND.

FACTORING BINOMIALS.

Entry Task What is the polynomial function in standard form with the zeros of 0,2,-3 and -1?

Special Factoring Patterns Students will be able to recognize and use special factoring patterns.

Warm - up Factor: 1. 4x 2 – 24x4x(x – 6) 2. 2x x – 21 (2x – 3)(x + 7) 3. 4x 2 – 36x + 81 (2x – 9) 2 Solve: 4. x x + 25 = 0x = x 2 +

Section 6.3 Special Factoring. Overview In this section we discuss factoring of special polynomials. Special polynomials have a certain number of terms.

Factoring Polynomials. 1.Check for GCF 2.Find the GCF of all terms 3.Divide each term by GCF 4.The GCF out front 5.Remainder in parentheses Greatest Common.

Factoring trinomials ax² + bx +c a = any number besides 1 and 0.

Keep in Your Notes!! list the first 15 perfect squares 1² = 2² = 3² =

Warm Up Factor out the GCF 1.-5x x x 3 +4x Factor 3. 4.

5-4 Factoring Quadratic Expressions Hubarth Algebra II.

Objective The student will be able to:

Factoring Quadratic Expressions Lesson 4-4 Part 2

Factoring Special Cases

Special Factoring Formulas

Do Now Determine if the following are perfect squares. If yes, identify the positive square root /16.

What numbers are Perfect Squares?

Factoring the Difference of Two Squares

Factoring Special Cases :

FACTORING BINOMIALS Section 4.3

Factor. x2 – 10x x2 – 16x + 1 Multiply. 3. (4x- 3y)(3x +4y)

Answers to Homework 8) (x + 6)(2x + 1) 10) (2n – 3)(2n – 1) 12) (2r – 5)(3r – 4) 14) (5z – 1)(z + 4) 16) (2t – 1)(3t + 5) 18) (4w + 3)(w – 2) 20) (2x +

Factoring Using Special Patterns

Show What You Know! x2 + 4x – 12 5x2 + 19x x2 – 25x - 25

Factoring GCF and Trinomials.

Factoring Differences of Squares

Perfect Square Trinomials

Objective The student will be able to:

Factoring Review Review Tying it All Together

AA Notes 4.3: Factoring Sums & Differences of Cubes

Objective The student will be able to:

AA-Block Notes 4.4: Factoring Sums & Differences of Cubes

Objective The student will be able to:

10. Solving Equations Review

Objective The student will be able to:

ALGEBRA I - SECTION 8-7 (Factoring Special Cases)

Objective The student will be able to:

10. Solving Equations Review

Factoring Differences of Squares

4 Steps for factoring Difference of Squares

Solving the Quadratic Equation by Completing the Square

Objective The student will be able to:

Objective The student will be able to:

Objective The student will be able to:

Factoring Quadratic Trinomials Part 1 (when a=1 and special cases)

Objective The student will be able to:

Factoring Polynomials

Presentation transcript:

FACTORING SPECIAL CASES

The vocabulary of perfect squares Perfect squares are numbers like 4, 9, 16, 25, etc. Any variable to an even power is a perfect square. X 2, Y 4, A 6, D 8 are all perfect squares 4x 2 is a perfect square (2x)(2x) (3y) 2 is a perfect square (3y)(3y) The word ‘difference’ means ‘subtract’

The difference of perfect squares X 2 – 9 (difference of perfect squares) AC number is (1)(9) = 9 B = 0 (no x term) - 9 SUBTRACT You need 2 numbers that multiply to give 9 and subtract to give 0 ( + 3 and – 3 ) X 2 + 3x – 3x – 9 = x(x + 3) – 3(x + 3) (x + 3)( x – 3 )

Shortcut! X 2 – 9 = (x + 3)( x – 3 ) Square root 1st + square root 2 nd Square root 1st - square root 2 nd Pattern is always the same

More examples 4X = (2x + 3)(2x – 3) 25x 2 – 64y 2 = (5x + 8y)(5x - 8y) 36x 2 – 144 = 36(x 2 – 4) = 36(x+2)(x-2) See how much easier it is when you factor out the greatest common factor first!

The sum of perfect squares Unless you can pull out a GCF, they are PRIME 4X Prime 25x y 2 = Prime 36x = 36(x 2 + 4) See how much easier it is when you factor out the greatest common factor first!

Perfect square trinomials Look for the pattern: 4X x + 9 4X 2 is a perfect square (+2x)(+2x) 9 is a perfect square (+3)(+3) (+2x)(+3) = +6x doubled = +12x 4X x + 9 = (2x+3)(2x+3)

Watch your signs! 4X x + 9 4X 2 is a perfect square (+2x)(+2x) 9 is a perfect square (-3)(-3) (+2x)(-3) = -6x doubled = -12x 4X x + 9 = (2x-3)(2x-3)

Look for the pattern! 4X x + 9 First and last are perfect squares Middle is double the product of their roots Last number is always positive Signs in the parentheses match middle sign 4X x + 9 = (2x-3)(2x-3) 4X x + 9 = (2x+3)(2x+3)

Fallback plan These special cases are faster to do if you recognize them and remember the ‘formula’. They can also be solved by the same grouping method that we have used for all other trinomials. 4X = (2x + 3)(2x - 3) 4X PRIME 4X x + 9 = (2x - 3)(2x - 3) 4X x + 9 = (2x + 3)(2x + 3)

Difference of perfect square Sum of perfect squares Perfect square trinomials You can write the answer just by looking at them if you can: recognize them remember the formula They also work out just fine if you do them the old-fashioned way ~ it just takes longer.