# Answer to Question #12600 in Algebra for Lauren

Question #12600

36X^2+30X-36 is the product of 6X-4 and what other factor?

Expert's answer

36X^2+30X-36=6(6x^2+5x-6)

6x^2+5x-6=0

x1,2=(-5+-sqrt(25+144))/12=(-5+-sqrt(169))/12=(-5+-13)/12

so x1=(-5+13)/12=8/12=2/3

x2=(-5-13)/12=-18/12=-3/2

Therefore 6x^2+5x-6=6(x-2/3)(x+3/2)=(3x-2)(2x+3)

So 36X^2+30X-36=6(6x^2+5x-6)=6(3x-2)(2x+3)=(6x-4)(6x+9)

Thus, the second factor is (6x+9)

6x^2+5x-6=0

x1,2=(-5+-sqrt(25+144))/12=(-5+-sqrt(169))/12=(-5+-13)/12

so x1=(-5+13)/12=8/12=2/3

x2=(-5-13)/12=-18/12=-3/2

Therefore 6x^2+5x-6=6(x-2/3)(x+3/2)=(3x-2)(2x+3)

So 36X^2+30X-36=6(6x^2+5x-6)=6(3x-2)(2x+3)=(6x-4)(6x+9)

Thus, the second factor is (6x+9)

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