b Trinomial Quadratic Equation ax 2 bx c Fill the 2 empty sides with 2 numbers that are factors of ac and add to give you b X Box 20 9 Trinomial Quadratic Equation ID: 628815
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Slide1
X-box FactoringSlide2
X- Box
Product of a & c
b
Trinomial (Quadratic Equation)
ax
2
+ bx + c
Fill the 2 empty sides with 2 numbers that are factors of ‘a·c’ and add to give you ‘b’. Slide3
X- Box
20
9
Trinomial (Quadratic Equation)
x
2
+ 9x + 20
Fill the 2 empty sides with 2 numbers that are factors of ‘a·c’ and add to give you ‘b’.
4
5Slide4
X- Box
-42
-1
Trinomial (Quadratic Equation)
2x
2
-x - 21
Fill the 2 empty sides with 2 numbers that are factors of ‘a·c’ and add to give you ‘b’.
-7
6Slide5
X-box Factoring
This is a guaranteed method for factoring quadratic equations—no guessing necessary!
We will learn how to factor quadratic equations using the x-box methodSlide6
LET’S TRY IT!
Students apply basic factoring techniques to second- and simple third-degree polynomials. These techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials.
Objective: I can use the x-box method to factor non-prime trinomials.Slide7
Factor the x-box way
Example: Factor x
2
-3x -10
-3
(1)(-10)=
-10
-5
2
-10
-5x
2x
x
2
x
-5
x
+2
x
2
-3x -10 = (x-5)(x+2)
GCF
GCF
GCF
GCFSlide8
Factor the x-box way
Middle
b=
m
+
n
Sum
Product
ac=mn
m
n
First and Last Coefficients
y =
ax
2
+ bx +
c
Last term
1st Term
Factor
n
Factor
m
Base 1
Base 2
GCF
HeightSlide9
Factor the x-box way
Example: Factor 3x
2
-13x -10
-13
-30
-15
2
-10
-15x
2x
3x
2
x
-5
3x
+2
3x
2
-13x -10 = (x-5)(3x+2)Slide10
Examples
Factor using the x-box method.
1. x
2
+ 4x – 12
a) b)
x
-12
4
6
-2
x
2
6
x
-2
x -12
x
-2
+6
Solution: x
2
+ 4x – 12 = (x
+ 6
)(x
- 2
)Slide11
Examples
continued
2. x
2 - 9x + 20
a) b)
20
-9
x
2
-4
x
-5
x 20
x
x
-4
-5
Solution: x
2
- 9x + 20
=
(x
- 4
)(x
- 5
)
-4
-5
Slide12
Examples
continued
3. 2x
2 - 5x - 7
a) b)
-14
-5
2x
2
-
7
x
2
x -7
x
2x
-7
+1
Solution: 2x
2
- 5x – 7 = (2x
- 7
)(x
+ 1
)
-7
2
Slide13
Examples
continued
3. 15x
2 + 7x - 2
a) b)
-30
7
15x
2
10
x
-3
x -2
5x
3x
+2
-1
Solution: 15x
2
+ 7x – 2 = (3x
+ 2
)(5x
- 1
)
10
-3
Slide14
Extra Practice
x
2
+4x -32
4x2 +4x -33x2
+ 11x – 20Slide15
Reminder!!
Don’t forget to check your answer by multiplying!