Download 4.3 Solve x² + bx + c = 0 by Factoring Objective: Solve quadratic

4.3 Solve x² + bx + c = 0 by Factoring
Objective: Solve quadratic equations
Vocabulary
Monomial:
Binomial:
Trinomial:
Factoring
Example: Factor x² - 9x + 20
Steps:
1. Identify c.
2. Make a list of things you can multiply to get c (integers only).
3. Looking at the list, find the factors that sum to b.
4. Write the quadratic in factored form.
Additional Examples:
1. x² - 3x – 18
2. r² + 2r – 63
3. x² + 14x + 48
4. x² + x -2
5. x² - 14x + 24
Not everything can be factored:
4. n² - 3n + 9
5. x² - 9x – 5
Special Situations
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Difference of Two Squares: a² - b² = (a + b)(a – b)
o Example x² - 9 = (x + 3)(x – 3)
Perfect Square Trinomial: a² + 2ab + b² = (a + b)²
o Example: x² + 6x + 9 = (x + 3)²
a² - 2ab + b² = (a - b)²
o
Example: x² - 4x + 4 = (x – 2)²
More Examples:
1. x² - 49
2. x² - 4
3. q² - 100
4. d² + 12d + 36
5. x² - 26x + 169
6. y² + 16y + 64
7. x² - 18x + 81
Solving Quadratic Equations
Zeros/Roots/x-intercepts: solutions to a quadratic equations. To solve by factoring, split up factors and
set each = 0. Solve each. Should always have two answers (although sometimes the same answer occurs
twice).
Examples: Find the roots of the equation.
1. x² - 5x – 36 = 0
2. x² - x – 42 = 0
3. x² + 19x + 84 = 0
4. u² - 9u = 0
5. m² = 7m
6. 14x – 49 = x²
Example 4: A town has a nature preserve with a rectangular field that measures 600 meters by 400
meters. The town wants to double the area of the field by adding land as shown. Find the new
dimensions of the field.
Extra Example 4: You have a rectangular vegetable garden in your backyard that measures 15 feet by 10
feet. You want to double the area by adding the same distance x to the length and the width of the
garden. Find the value of x and the new dimensions of the garden.
Finding the zeros of a function by re-writing it in intercept form: Make sure it is solved for y. Change y to
0 and solve as normal.
Examples:
1. y = x² - x – 12
2. y = x² + 12x + 36
3. y = x² + 5x – 14
4. y = x² - 7x – 30
5. f(x) = x² – 10x + 25
Homework: 1, 2 – 8 ev, 16 – 20 ev, 23, 28 – 38 ev, 44 – 54 ev, 60, 66, 67, 69-71