SOLUTION: Megan factored the expression -12x^2+52x-35 as (-2x+5)(6x-7) But when Jacob applied the FOIL principle and multiplied out (-2x+5)(6x-7) he got -12x^2+44x-35; thus, Megan’s solution

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Megan factored the expression -12x^2+52x-35 as (-2x+5)(6x-7) But when Jacob applied the FOIL principle and multiplied out (-2x+5)(6x-7) he got -12x^2+44x-35; thus, Megan’s solution      Log On


   

Question 623972: Megan factored the expression -12x^2+52x-35 as (-2x+5)(6x-7) But when Jacob applied the FOIL principle and multiplied out (-2x+5)(6x-7) he got -12x^2+44x-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 lenny460(1073) About Me  (Show Source):
You can put this solution on YOUR website!
Factor:

-12x^2 + 52x - 35

Factor a trinomial:

-(6x - 5)(2x -7)

Multiply the above using FOIL Method:
6x * 2x = 12x^2
6x * -7 = -42x
-5 * 2x = -10x
-5 * -7 = 35

12x^2 - 42x - 10x + 35
Combine like terms:
-42x - 10x = -52x

-1(12x^2 - 52x + 35)
-1 * 12x^2 = -12x^2
-1 * -52x = 52x
-1 * 35 = -35

We therefore get:

-12x^2 + 52x - 35

The Factors are:

-(6x - 5)(2x - 7)


There is another way to factor:

-12x^2 + 52x - 35
The factors are:

(-7 + 2x)(5 - 6x)

Let's check by the FOIL Method:

-7 * 5 = -35
-7 * -6x = 42x
2x * 5 = 10x
2x * -6x = -12x^2

-35 + 42x + 10 x - 12x^2

Combine like terms:
42x + 10x = 52x

-35 + 52x - 12x^2 or

-12x^2 + 52x - 35


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