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8.4 – Factoring Trinomials: a x 2 + b x + c. Recall : Factor x 2 + 5 x + 6. Recall : Factor x 2 + 5 x + 6 ( x )( x ). Recall : Factor x 2 + 5 x + 6 ( x )( x ) x 2 + 2 x + 3 x + 6 *2 factors of 6 that add up to 5!. - PowerPoint PPT Presentation
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8.4 – Factoring Trinomials: ax2 + bx + c
Recall: Factor x2 + 5x + 6
Recall: Factor x2 + 5x + 6
(x )(x )
Recall: Factor x2 + 5x + 6
(x )(x )
x2 + 2x + 3x + 6
*2 factors of 6 that add up to 5!
Recall: Factor x2 + 5x + 6
(x )(x )
x2 + 2x + 3x + 6
*2 factors of 6 that add up to 5!
Factor 2x2 + 7x + 6.
Recall: Factor x2 + 5x + 6
(x )(x )
x2 + 2x + 3x + 6
*2 factors of 6 that add up to 5!
Factor 2x2 + 7x + 6.
*2 factors of 12 that add up to 7!
Recall: Factor x2 + 5x + 6
(x )(x )
x2 + 2x + 3x + 6
*2 factors of 6 that add up to 5!
Factor 2x2 + 7x + 6.
*2 factors of 12 that add up to 7!
2x2 + x + x + 6
Recall: Factor x2 + 5x + 6
(x )(x )
x2 + 2x + 3x + 6
*2 factors of 6 that add up to 5!
Factor 2x2 + 7x + 6.
*2 factors of 12 that add up to 7!
2x2 + x + x + 6
2x2 + 4x + 3x + 6
Recall: Factor x2 + 5x + 6(x )(x )
x2 + 2x + 3x + 6*2 factors of 6 that add up to 5!
Factor 2x2 + 7x + 6. *2 factors of 12 that add up to 7! 2x2 + x + x + 62x2 + 4x + 3x + 62x(x + 2) + 3(x + 2)
Recall: Factor x2 + 5x + 6(x )(x )
x2 + 2x + 3x + 6*2 factors of 6 that add up to 5!
Factor 2x2 + 7x + 6. *2 factors of 12 that add up to 7! 2x2 + x + x + 62x2 + 4x + 3x + 62x(x + 2) + 3(x + 2)
(x + 2)(2x + 3)
Ex. 1 Factor 4x2 + 14x – 8.
Ex. 1 Factor 4x2 + 14x – 8.
2(2x2 + 7x – 4)
Ex. 1 Factor 4x2 + 14x – 8.
2(2x2 + 7x – 4)
2[2x2 + x + x – 4]
Ex. 1 Factor 4x2 + 14x – 8.
2(2x2 + 7x – 4)
2[2x2 + x + x – 4]
2[2x2 – x + 8x – 4]
Ex. 1 Factor 4x2 + 14x – 8.
2(2x2 + 7x – 4)
2[2x2 + x + x – 4]
2[2x2 – x + 8x – 4]
2[x(2x – 1) + 4(2x – 1)]
Ex. 1 Factor 4x2 + 14x – 8.
2(2x2 + 7x – 4)
2[2x2 + x + x – 4]
2[2x2 – x + 8x – 4]
2[x(2x – 1) + 4(2x – 1)]
2[(2x – 1)(x + 4)]
Ex. 1 Factor 4x2 + 14x – 8.
2(2x2 + 7x – 4)
2[2x2 + x + x – 4]
2[2x2 – x + 8x – 4]
2[x(2x – 1) + 4(2x – 1)]
2[(2x – 1)(x + 4)]
Ex. 2 Factor 2x2 – 5x + 2.
Ex. 1 Factor 4x2 + 14x – 8.
2(2x2 + 7x – 4)
2[2x2 + x + x – 4]
2[2x2 – x + 8x – 4]
2[x(2x – 1) + 4(2x – 1)]
2[(2x – 1)(x + 4)]
Ex. 2 Factor 2x2 – 5x + 2.
2x2 + x + x + 2
Ex. 1 Factor 4x2 + 14x – 8.2(2x2 + 7x – 4)2[2x2 + x + x – 4] 2[2x2 – x + 8x – 4] 2[x(2x – 1) + 4(2x – 1)]2[(2x – 1)(x + 4)]
Ex. 2 Factor 2x2 – 5x + 2. 2x2 + x + x + 2 2x2 – x – 4x + 2
Ex. 1 Factor 4x2 + 14x – 8.
2(2x2 + 7x – 4)
2[2x2 + x + x – 4]
2[2x2 – x + 8x – 4]
2[x(2x – 1) + 4(2x – 1)]
2[(2x – 1)(x + 4)]
Ex. 2 Factor 2x2 – 5x + 2.
2x2 + x + x + 2
2x2 – x – 4x + 2
x(2x – 1) – 2(2x – 1)
Ex. 1 Factor 4x2 + 14x – 8.
2(2x2 + 7x – 4)
2[2x2 + x + x – 4]
2[2x2 – x + 8x – 4]
2[x(2x – 1) + 2(2x – 1)]
2[(2x – 1)(x + 2)]
Ex. 2 Factor 2x2 – 5x + 2.
2x2 + x + x + 2
2x2 – x – 4x + 2
x(2x – 1) – 2(2x – 1)
(2x – 1)(x – 2)
Ex. 3 Solve 8a2 – 9a – 5 = 4 – 3a. Check your solutions.
Ex. 3 Solve 8a2 – 9a – 5 = 4 – 3a. Check your solutions.
8a2 – 9a – 5 = 4 – 3a
Ex. 3 Solve 8a2 – 9a – 5 = 4 – 3a. Check your solutions.
8a2 – 9a – 5 = 4 – 3a
+3a -4 -4 + 3a
Ex. 3 Solve 8a2 – 9a – 5 = 4 – 3a. Check your solutions. 8a2 – 9a – 5 = 4 – 3a
+3a -4 -4 + 3a
8a2 – 6a – 9 = 0
Ex. 3 Solve 8a2 – 9a – 5 = 4 – 3a. Check your solutions. 8a2 – 9a – 5 = 4 – 3a
+3a -4 -4 + 3a
8a2 – 6a – 9 = 0
8a2 + a + a – 9 = 0
Ex. 3 Solve 8a2 – 9a – 5 = 4 – 3a. Check your solutions. 8a2 – 9a – 5 = 4 – 3a
+3a -4 -4 + 3a
8a2 – 6a – 9 = 0
8a2 + a + a – 9 = 0
8a2 – 12a + 6a – 9 = 0
Ex. 3 Solve 8a2 – 9a – 5 = 4 – 3a. Check your solutions. 8a2 – 9a – 5 = 4 – 3a
+3a -4 -4 + 3a
8a2 – 6a – 9 = 0
8a2 + a + a – 9 = 0
8a2 – 12a + 6a – 9 = 0
4a(2a – 3) + 3(2a – 3) = 0
Ex. 3 Solve 8a2 – 9a – 5 = 4 – 3a. Check your solutions. 8a2 – 9a – 5 = 4 – 3a
+3a -4 -4 + 3a
8a2 – 6a – 9 = 0
8a2 + a + a – 9 = 0
8a2 – 12a + 6a – 9 = 0
4a(2a – 3) + 3(2a – 3) = 0
(2a – 3)(4a + 3) = 0
Ex. 3 Solve 8a2 – 9a – 5 = 4 – 3a. Check your solutions. 8a2 – 9a – 5 = 4 – 3a
+3a -4 -4 + 3a 8a2 – 6a – 9 = 0 8a2 + a + a – 9 = 0 8a2 – 12a + 6a – 9 = 0 4a(2a – 3) + 3(2a – 3) = 0
(2a – 3)(4a + 3) = 02a – 3 = 0 4a + 3 = 0
Ex. 3 Solve 8a2 – 9a – 5 = 4 – 3a. Check your solutions. 8a2 – 9a – 5 = 4 – 3a
+3a -4 -4 + 3a 8a2 – 6a – 9 = 0 8a2 + a + a – 9 = 0 8a2 – 12a + 6a – 9 = 0 4a(2a – 3) + 3(2a – 3) = 0
(2a – 3)(4a + 3) = 02a – 3 = 0 4a + 3 = 0 2a = 3 4a = -3
Ex. 3 Solve 8a2 – 9a – 5 = 4 – 3a. Check your solutions. 8a2 – 9a – 5 = 4 – 3a
+3a -4 -4 + 3a 8a2 – 6a – 9 = 0 8a2 + a + a – 9 = 0 8a2 – 12a + 6a – 9 = 0 4a(2a – 3) + 3(2a – 3) = 0
(2a – 3)(4a + 3) = 02a – 3 = 0 4a + 3 = 0 2a = 3 4a = -3
a = 3/2 a = -3/4
