Factoring Trinomials Bustin’ da B ax2 + bx + c.

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Presentation transcript:

Factoring Trinomials Bustin’ da B ax2 + bx + c

What 2 numbers when multiplied together give you 24,and when added give you -14?

ax2 + bx + c Multiply a and c together, place that value here Place the b value here Then ask, what 2 numbers when multiplied together give you a times c, when added give you b? Place the answers to your question here.

Ex. 2x2+10x+12 a times c =24 b = 10 What 2 numbers when multiplied together give you 24,and when added give you 10? 4 and 6 24 6 4 10

Fill out the cross for these 4 examples 10x2 + 27x + 5 14x2 + 16x + 2 6x2 + 17x + 7 3x2 + 25x + 8

Use these results to bust da b. 24 6 4 10 ax2 + bx + c 2x2+10x+12 b= 10 or 4 + 6 4 and 6 were my previous results So now bust da b, 10x is now 6x + 4x 2x2+10x+12 2x2+6x+4x+12 Now factor this by grouping!! (2x2+6x)+(4x+12) 2x(x+3)+4(x+3) (2x+4)(x+3) 2(x+2)(x+3)

Factor 3x2 -7x -6 3x2 -7x -6 3x2 -9x + 2x -6 (3x2 -9x) + (2x -6) a times c = -18, b = -7 So, what numbers when multiplied together give you -18 when added together give you -7? -18 2 -9 -7 -9 and 2 3x2 -7x -6 3x2 -9x + 2x -6 (3x2 -9x) + (2x -6) 3x(x -3) + 2(x -3)

Factor 3x2 + 11x + 6 3x2 + 9x+2x + 6 (3x2 + 9x)+(2x + 6) 18 Factor 3x2 + 11x + 6 9 2 11 3x2 + 9x+2x + 6 (3x2 + 9x)+(2x + 6) 3x(x+3) +2(x+3) (3x +2)(x+3) What 2 numbers when multiplied together give you 18,and when added give you 11? 9 and 2

Factor 4x2 - 14x + 6 24 -12 -2 -14 Since a times c is positive and b is negative both answers must be negative 4x2 - 14x + 6 4x2 - 12x -2x + 6 (4x2 - 12x) (-2x + 6) 4x(x - 3) -2(x - 3) (4x - 2)(x - 3) 2(x - 2)(x - 3) + 2 is the gcf of (4x-2) What 2 numbers when multiplied together give you 24,and when added give you -14? -12 and -2

Factor - 8x2 - 47x + 6 - 8x2 - 47x + 6 - 8x2 - 48x+1x + 6 -48 Factor - 8x2 - 47x + 6 -48 1 -47 - 8x2 - 47x + 6 - 8x2 - 48x+1x + 6 - 8x(x+ 6)+1(x + 6) (-8x+1)(x+6) What 2 numbers when multiplied together give you -48,and when added give you -47? -48 and 1

Factor 36x2 - 1 rewrite so 36x2 + 0x - 1 36x2 + 6x -6x - 1 -36 6 -6 rewrite so 36x2 + 0x - 1 36x2 + 6x -6x - 1 (36x2 + 6x)+(-6x - 1) 6x(6x + 1)+-1(6x +1) (6x -1) (6x +1) What 2 numbers when multiplied together give you -36,and when added give you 0? -6 and 6