Question 622656: Megan factored the expression 18x^2-57x+35 as (6x-7)(3x-5) But when Jacob applied the FOIL principle and multiplied out (6x-7)(3x-5), he got 18x^2-51x+35; thus, Megan’s solution does not appear to check. Why is that? Please help Megan to understand this better. Explain your reasoning and correctly factor the original expression, if possible. If the expression is prime, so state
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! The correct factors are (3x-7)(6x-5)
She had (6x-7)(3x-5)
when multiplying by foil, (6x-7)(3x-5) equals:
18x*2 - 30x - 21x + 35 which equals:
18x^2 - 51x + 35
when multiplying by foil, (3x-7)(6x-5) equal:
18x^2 - 15x - 42x + 35 which equals:
18x^2 - 57x + 35
She got the coefficients right (3x and 6x) and she got the constants right (7 and 5), but she put them in the wrong places.
factors she used were:
(3x-7)(6x-5)
correct use of the factors was:
(6x-7)(3x-5)
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