Warmup Factor 3n3 – 12n2 – 30n Answer 3n(n2 – 4n -10)

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Presentation transcript:

Warmup Factor 3n3 – 12n2 – 30n Answer 3n(n2 – 4n -10)

Warm Up Magic Diamonds – find two numbers whose product match the number on top and whose sum matches the number on the bottom 16 16 -16 16 4 4 -4 4 -4 -4 8 2 -8 10 8 3 -1 -3 Can you do this one? -4

Lesson 7.3A Learning Target: Factor polynomials in the form ax2+bx+c

Quadratic Equation Any equation of the form ax2 + bx + c EXAMPLE: 5x2 – 4x + 6 a = 5 b = -4 c = 6

Know your A, B, C’s… ax2 + bx + c Quadratic Equation (standard form): Find the a, b, c’s of each: x2 + 7x + 12 x2 + 6x – 16 3. x2 – 6x 4. 3x2 + 7x + 12 5. 10x2 – 6x – 16 6. 4x2 - 16 a = 3 b = 7 c = 12 a = 1 b = 7 c = 12 a = 1 b = 6 c = -16 a = 10 b = -6 c = -16 a = 1 b = - 6 c = 0 a = 4 b = 0 c = -16

How can we factor x2 + 9x + 20 ? x2 9x 20 ? No common factors (except 1) x2 9x 20 ? Use the X-box method to turn these 3 terms into 4 terms!

Can We Use Boxes? YES! ax2 + bx + c a·c X ?? ?? b

EX 1: x2 + 9x + 20 a = 1 b = 9 c = 20 Find two numbers with: product of 20 sum of 9 1,20 -1,-20 2,10 -2,-10 4,5 -4, -5 a·c 20 X 5 4 9 b These fill in the other boxes!

Use the sides of the “X” to find the missing terms in the box… x2 + 9x + 20 Use the sides of the “X” to find the missing terms in the box… 20 X 5 4 x 5 9 x x2 5x Factored Form? ( x + 5 )( x + 4 ) 4x 20 4

Did you master today’s objective? x2 + 12x + 35 x2 – 12x + 32 x2 – x – 6 (x + 7)(x + 5) (x – 8)(x – 4) (x – 3)(x +2)

Assignment 7-3a: