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Drupady [299]
3 years ago
5

Factor completely 6n2 – 11n – 10

Mathematics
1 answer:
Pepsi [2]3 years ago
4 0

Step-1 : Multiply the coefficient of the first term by the constant   6 • -10 = -60

Step-2 : Find two factors of  -60  whose sum equals the coefficient of the middle term, which is   -11 .

     -60    +    1    =    -59

     -30    +    2    =    -28

     -20    +    3    =    -17

     -15    +    4    =    -11    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -15  and  4

                    6n2 - 15n + 4n - 10

Step-4 : Add up the first 2 terms, pulling out like factors :

                   3n • (2n-5)

             Add up the last 2 terms, pulling out common factors :

                   2 • (2n-5)

Step-5 : Add up the four terms of step 4 :

                   (3n+2)  •  (2n-5)

            Which is the desired factorization

Final result :

 (2n - 5) • (3n + 2)

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Answer:

\lim_{x \to 0} \frac{\frac{1}{6+x}-\frac{1}{6}}{x}=-1/36

Step-by-step explanation:

So we have the limit:

\lim_{x \to 0} \frac{\frac{1}{6+x}-\frac{1}{6}}{x}

Let's remove the fractions in the denominator by multiplying both layers by (6+x)(6). So:

\lim_{x \to 0} \frac{\frac{1}{6+x}-\frac{1}{6}}{x}\cdot (\frac{(6+x)(6)}{(6+x)(6)})

Distribute:

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Both the numerator and the denominator have an x. Cancel:

=\lim_{x \to 0} \frac{-1}{(6+x)(6)}

Direct substitution:

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Simplify:

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And that's our answer.

And we're done!

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