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3 years ago

Factor completely, the expression: 2x^3-2x^2-12x

1 answer:

muminat3 years ago

8 0

$2x^3-2x^2-12x=2x(x^2-x-6)=(*)\\\\------------------------------\\x^2-x-6\\\\a=1;\ b=-1;\ c=-6\\\\\Delta=(-1)^2-4\cdot1\cdot(-6)=1+24=25\\\\\sqrt\Delta=\sqrt{25}=5\\\\x_1=\frac{1-5}{2\cdot1}=\frac{-4}{2}=-2;\ x_2=\frac{1+5}{2\cdot1}=\frac{6}{2}=3\\\\x^2-x-6=(x+2)(x-3)\\\\------------------------------\\\\(*)=2x(x+2)(x-3)$

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Answer:

______________________________________________________

TRIGONOMETRY IDENTITIES TO BE USED IN THE QUESTION :-

For any right angled triangle with one angle α ,

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SOME GENERAL TRIGNOMETRIC FORMULAS :-

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______________________________________________________

Now , lets come to the question.

In a right angled triangle , let one angle be α (in place of theta) .

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$=> \sin\alpha \times \frac{1}{\cos\alpha }$

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Step-by-step explanation:

I find it takes less work if I can eliminate obviously wrong answers. Toward that end, we can consider the constant terms only:

-3 +(-2) = -5 . . . . possible equivalent
-10 -5 = -15 . . . . NOT equivalent
3(-5) -2(5) = -25 . . . . NOT equivalent
-9 -(-4) = -5 . . . . possible equivalent
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Now, we can go back and check the other terms in the candidate expressions we have identified.

1. (-16x² +10x -3) +(4x² -29x -2) = (-16+4)x² +(10-29)x -5 = -12x² -19x -5 . . . OK

4. (2x² -11x -9) -(14x² +8x -4) = (2-14)x² +(-11-8)x -5 = -12x² -19x -5 . . . OK

6. 2(x -1) -3(4x² +7x +1) = -12x² +(2 -3·7)x -5 = -12x² -19x -5 . . . OK

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