unit 2 – quadratic, polynomial, and radical equations and inequalities

Unit 2 – Quadratic, Polynomial, and Radical Equations and

InequalitiesChapter 5 – Quadratic Functions and Inequalities5.3 – Solving Quadratic Equations by Factoring

5.3 – Solving Quadratic Equations by Factoring

In this section we will learn how to:Write quadratic equations in intercept form

Solve quadratic equations by factoring

5.3 – Solving Quadratic Equations by Factoring

Intercept form – of a quadratic equation is y = a(x – p)(x – q)

p and q represent the x-intercepts of the graph corresponding to the equation

5.3 – Solving Quadratic Equations by Factoring

Changing a quadratic in intercept form to standard forms requires using the FOIL methodFirstOuterInnerLast

Multiply the terms: first, outer, inner, lastCombine any like terms

5.3 – Solving Quadratic Equations by Factoring

Example 1(6x + 1)(2x – 4)

5.3 – Solving Quadratic Equations by Factoring

Example 2(-3x + 5)(3x + 2)

5.3 – Solving Quadratic Equations by Factoring

Example 3(9x – 2)2

5.3 – Solving Quadratic Equations by Factoring

Example 4(6x + 3)2

5.3 – Solving Quadratic Equations by Factoring

Example 5(x + 7)3

5.3 – Solving Quadratic Equations by Factoring

Example 6(2x + 4)3

5.3 – Solving Quadratic Equations by Factoring

Example 7(3x – 1)3

5.3 – Solving Quadratic Equations by Factoring

HOMEWORK

5.3 Part 1 Worksheet

5.3 – Solving Quadratic Equations by Factoring

Find the Greatest Common Factor (GCF)

If all the terms of a polynomial have a factor(s) in common, you can factor out that greatest common factor

5.3 – Solving Quadratic Equations by Factoring

Example 1Factor out the GCF

8y2 + 16y5 =

6a4 – 8a2 + 2a =

-15x3y + 9x2y7 =

-5x2y – x2 + 3x3y5 + 11x7 =

5.3 – Solving Quadratic Equations by Factoring

CLASSWORK

5.3 Part 2 Practice

5.3 – Solving Quadratic Equations by Factoring

Factoring a Difference of Perfect Squares

If you have a quadratic equation that has the difference of two terms that are both perfect squares, it factors as:

A2 – B2 = (A + B)(A – B)

5.3 – Solving Quadratic Equations by Factoring

Example 1Factor:

x2 – 9 =

4x2 – 25 =

9x2 – 16y2 =

5.3 – Solving Quadratic Equations by Factoring

Example 2Factor:

100x2 – 81y2 =

3x2 – 75 =

20x2 – 5y2 =

5.3 – Solving Quadratic Equations by Factoring

CLASSWORK/HOMEWORK

5.3 Graded Worksheet

5.3 – Solving Quadratic Equations by Factoring

Factoring a TrinomialAx2 ± Bx + C =

ADD inner and outer to get B

( + ) ( + )( - ) ( - )

5.3 – Solving Quadratic Equations by Factoring

Example 1Factor:

x2 + 10x + 9

x2 + 8x + 15

x2 – 10x + 25

5.3 – Solving Quadratic Equations by Factoring

Example 2Factor:

x2 – 2x + 1

x2 – 14x + 24

x2 + 6x + 9

5.3 – Solving Quadratic Equations by Factoring

HOMEWORK

5.3 Part 3 Practice

5.3 – Solving Quadratic Equations by Factoring

Factoring a TrinomialAx2 ± Bx - C =

SUBTRACT inner and outer to get B

( + ) ( - )( - ) ( + )

5.3 – Solving Quadratic Equations by Factoring

Example 1Factor:

x2 – 3x – 18

x2 + 5x – 6

x2 – 2x – 35

5.3 – Solving Quadratic Equations by Factoring

Example 2Factor:

x2 + 4x – 21

x2 + x – 20

x2 – 4x – 5

5.3 – Solving Quadratic Equations by Factoring

HOMEWORK

5.3 Part 4 Worksheet

5.3 – Solving Quadratic Equations by Factoring

Factoring a TrinomialAx2 ± Bx + C

( + ) ( + )( - ) ( - )

Ax2 ± Bx – C( + ) ( - )( - ) ( + )

5.3 – Solving Quadratic Equations by Factoring

Example 1Factor:

2x2 + 3x + 1

5x2 – 28x – 12

5.3 – Solving Quadratic Equations by Factoring

Example 2Factor:

4x2 – 12x + 5

3x2 + 2x – 16

5.3 – Solving Quadratic Equations by Factoring

Example 3Factor:

4x2 – 14x + 10

15x2 + 18x – 24

5.3 – Solving Quadratic Equations by Factoring

Example 4Factor:

25x2 – 10x – 3

3x2 + 11x + 6

5.3 – Solving Quadratic Equations by Factoring

HOMEWORK

5.3 Part 5 Worksheet

5.3 – Solving Quadratic Equations by Factoring

CLASSWORK

5.3 Graded Worksheet

5.3 – Solving Quadratic Equations by Factoring

Solving by Factoring If the equation is not equal to zero, rewrite so that

it isFactor out a GCF if possibleYou now have one of the following:

A trinomial that must be factored (x2 + Bx + C)A difference of two squares that must be factored

(x2 – C)Two expressions

Set each of the remaining expressions equal to zero and solve

5.3 – Solving Quadratic Equations by Factoring

Example 1Factor and solve:

x2 + 13x + 30 = 0

x2 + 5x – 24 = 0

5.3 – Solving Quadratic Equations by Factoring

Example 2Factor and solve:

x2 – 13x = -22

x2 – 2x = 48

5.3 – Solving Quadratic Equations by Factoring

Example 3Factor and solve:

x2 – 100 = 0

2x2 – 72 = 0

5.3 – Solving Quadratic Equations by Factoring

Example 4Factor and solve:

x2 + 15x = 0

2x2 – 6x = 0

5.3 – Solving Quadratic Equations by Factoring

HOMEWORK

5.3 Worksheet

5.3 – Solving Quadratic Equations by Factoring

CLASSWORK

5.3 Graded Worksheet