Unit 2 – Quadratic, Polynomial, and Radical Equations and Inequalities
description
Transcript of 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