Factor completely 2x2 − 6x − 36.

1 answer:

4 0

To factor out completely, we should have reached the most simplified form,
first we should take out 2.
2(x2 - 3x - 18)
then we should factor out the inside of the parenthesis,
2(x - 6)(x + 3)
And that's the most simplified and factored out form.

The final answer is then the second option, 2(x − 6)(x + 3)

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What is the solution of x=2+ square root x-2?

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So I'm going to assume that this question is asking for non extraneous solutions, or solutions that are found in the equation and are valid solutions when plugged back into the equation. So firstly, subtract 2 on both sides of the equation:

$x-2=\sqrt{x-2}$

Next, square both sides:

$(x-2)^2=x-2\\(x-2)(x-2)=x-2\\x^2-4x+4=x-2$

Next, subtract x and add 2 to both sides of the equation:

$x^2-5x+6=0$

Now we are going to be factoring by grouping to find the solution(s). Firstly, what two terms have a product of 6x^2 and a sum of -5x? That would be -3x and -2x. Replace -5x with -2x - 3x:

$x^2-2x-3x+6=0$