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 Thursday 28th of September

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 Depdendent Variable

 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Factoring Completely General Quadratic Trinomials

 WHAT TO DO: HOW TO DO IT: Given a trinomial of type ax2 Â± bx Â± c that has at least one common factor. Factor out all of the common factors then look at the remaining quadratic trinomial. kÂ·(Ax 2 Â± Bx Â± C) Given a general trinomial: 72x 2 − 60x − 28 Factor out common factor if there is one. 4(18x 2 − 15x − 7) On Scratch Paper, look at polynomial inside (...): 18x 2 − 15x − 7 Use GN and Clue of Signs  Multiply first and last coefficients: GN 18Â·7 = 126 NOTE: Last sign is â€œ−â€ therefore Find all pairs of factors of 126 with difference of 15. The largest factor of the pair gets sign of middle term, â€œ − â€ the other is positive: − 21 and + 6 Rearrange polynomial using these values as coefficients of x 18x2 − 21x + 6x − 7 Factor common factor from each group: 3x(6x − 7) + 1(6x −7) Combine with first term factored out the complete factors of: 72x2 - 60x - 28 4(3x + 1)(6x − 7) answer Check by multiplying out: