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Lesson 3.4: Solve x2 + bx + c = 0 by factoring- Day 1
Essential Question
How do you use factoring to solve quadratic equations?
Monomial – an expression that is a number or variable
or a product of a number or variable
Binomial – the sum of two monomials
Trinomial – the sum of three monomials
Quadratic equation - ax2 + bx + c
Review Factoring:
3x(2x – 5) – 4(2x – 5)
(2x – 5)
(2x – 5)
(2x – 5)(3x – 4)
Ex 1. 3x (4x + 5) – 5(4x + 5) = _______ ( ___ - ___ )
Ex 2. 5z(2z + 1) + 2(2z + 1) = ______ ( ___ + ___ )
You Try: (x+3)(2x) + (x+3)(7)
Four Terms
• Grouping
- make 2 groups that are 2 terms each
- factor out the variable and number GCF’s of each
group
- factor out the binomial GCF
6x3 – 15x2 – 8x + 20
(6x3 – 15x2) +(–8x + 20)
3x2 3x2
-4 -4
3x2(2x – 5) + -4(2x – 5)
(2x – 5)
(2x – 5)
(2x – 5)(3x2 – 4)
Ex 3. 12x2 + 21x – 8x – 14 = 0
Ex 4. 8x2 + 24x – 14x – 42 = 0
You Try: 72x2 – 56x – 36x + 28 = 0
Lesson 3.4: Solve x2 + bx + c = 0 by factoring- Day 2
Review of factoring:
1. x2 – 16
2. x2 – 9
3. 4x2 – 1
4. 25x2 – 16y2
5. 3x2 – 75
6. x2 + y2
7. x2 + 2x + 1
8. x2-2x+3x-6
9. (x-1)(x) + 3(x-1)
Three terms
• Trinomials ax2+bx+c
use when there are 3 terms
- factor out GCF, if necessary
- figure out what multiplies to be a and c (leading
coefficient and the constant) and adds to be b (the
middle coefficient)
- rewrite the middle term as a sum of the two
factors
- factor the 4 terms by grouping
6x2 – 7x – 20
6x2 – 15x + 8x – 20
(6x2 – 15x) + (8x – 20)
3x(2x – 5) + 4(2x – 5)
(2x – 5)(3x + 4)
Ex 5. x2 + 7x + 10 = 0
You Try: x2 – 7x + 10 = 0
Ex 6. 6x2 + 11x + 3 = 0
You Try: 2x2 + 5x + 2 = 0
Ex 7. 2x2 – 24x + 72 = 0
You Try: x2 + 4x – 32 = 0
You Try: 3x2 – 5x = 0
You Try: x2 – 9 = 0
You Try: 4x2 – 8x + 3 = 0