Factoring Quadratics using X-Box method and Factor by Grouping.
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Transcript of Factoring Quadratics using X-Box method and Factor by Grouping.
Factoring Quadratics using X-Box
method and Factor by Grouping
Factoring Quadratics using X-Box
method and Factor by Grouping
Bell Ringer:
Homework!• Score out of 26• Divide by 2.6
X- Marks the Spot
factors factors
Producta∙c
Sumb
Solve using factoring by grouping
Example: Factor 3x2 -13x -10
-13
(3)(-10)=
-30
-15 2
-10
(3x2-15x)+(2x-
10)
=3x(x-5)+2(x-5)
=(x-5)(3x+2)
-15x+2x
3x2
-13x=
-15x+2x
1. Plug and solve values of our “X” 2. Substitute new factors in for bx
3. Solve by grouping!
4. Check answer:
3x2 -13x -10=(x-5)(3x+2)
(x-5)(3x+2)
Solve the x-box wayExample: Factor 3x2 -13x -10
-13
(3)(-10)=
-30
-15 2
-10
-15x
2x
3x2
x -5
3x
+2
3x2 -13x -10 (x-5)(3x+2)
FACTOR the x-box way
Middleb=m+
nSum
Product
ac=mnm n
First and Last
Coefficients
ax2 + bx + c
Last term
1st Term
Factorn
Factorm
GCF GCF
GCF
GCF
ExamplesExamplesFactor using the x-box method.1. x2 + 4x – 12
x -12
4 6 -2 x
-2
+6
Solution: x2 + 4x – 12 (x + 6)(x - 2)
2x
-12
-2x
6x
ExamplesExamples2. x2 - 9x + 20
20
-9
Solution: x2 - 9x + 20 (x - 4)(x - 5)
-4 -5
x2-4x-5x+20
=(x2-4x)+(-5x+20)
=x(x-4)-5(x-4)
=(x-4)(x-5)
ExamplesExamples3. 2x2 - 5x – 7
-14
-5
x
2x -7
+1
Solution: 2x2 - 5x – 7 (2x - 7)(x + 1)
-7 2
2x²
-7
-7x
2x
ExamplesExamples4. 15x2 + 7x – 2
-30
7
5x
3x +2
-1
Solution: 15x2 + 7x – 2 (3x + 2)(5x - 1)
10 -3
15x²
-2-3x
10x
• 2x2 +3x –9
• 6x2 + x – 2
• 4x2 + 9x + 2
You TryYou Try
Partner Activity!• On the front side of your Factoring Practice are your
questions. On the back side is the answer key for your partner.
• Work on your own Factoring Practice worksheet and when you want to check your answer, do so with your partner.
• Remember the purpose of this activity is to help each other to be able to solve the problems. Be good teachers! (Do not just give them the answers)
• Work on for the time given and get as far as you can!