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3 years ago

Factor 21x^2 - 37x + 12

1 answer:

8 0

Answer: (7x-3)(3x-4), rewrite 37x as 9x-28x and factor out 3x from 21x^2-9x. then factor out 7x-3 and you should be good. i hope this helped!

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3 years ago

2x - 5 > -9<br> solve inequality

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2 years ago

A 6am one morning the temperature was -14 degrees by noon it rose 8 degrees and then rose another 2 degrees by 3pm. By 6pm the t

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3 years ago

Let n be a natural number. Show that 3 | n3 −n

Vladimir [108]

Let $n=1$ . Then $n^3-n=1^3-1=0$ . By convention, every non-zero integer $n$ divides 0, so $3\vert n^3-n$ .

Suppose this relation holds for $n=k$ , i.e. $3\vert k^3-k$ . We then hope to show it must also hold for $n=k+1$ .

You have

$(k+1)^3-(k+1)=(k^3+3k^2+3k+1)-(k+1)=(k^3-k)+3(k^2+k)$

We assumed that $3\vert k^3-k$ , and it's clear that $3\vert 3(k^2+k)$ because $3(k^2+k)$ is a multiple of 3. This means the remainder upon divides $(k+1)^3-(k+1)$ must be 0, and therefore the relation holds for $n=k+1$ . This proves the statement.

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3 years ago