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viktelen [127]
3 years ago
9

Write a polynomial in standard form with zeros 1, 2, and −5.

Mathematics
1 answer:
Sonbull [250]3 years ago
6 0

Answer:

Step-by-step explanation:

First thing you have to do is write those zeros into factors.  If

x = 1, then its factor is (x - 1).  If

x = 2, then its factor is (x - 2).  If

x = -5, then its factor is (x + 5).

Now we FOIL them all together, starting with the first 2:

(x - 1)(x - 2) = x^2--2x-1x+2

Combine like terms to get

x^2-3x+2

Now FOIL that with the last factor to get

x^3-3x^2+2x+5x^2-15x+10

Combine like terms to get

x^3+2x^2-13x+10=0, which is choice C

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In order for a number to be divisible by 4, its last two digits must be divisible by 4. This will be the case if either of these conditions holds:

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We must count the ways these conditions can be met with the given digits.

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Since we only have even numbers to work with, the ones digit must be an even multiple of 2: 4 or 8. (The tens digit cannot be odd.) The digits 4 and 8 comprise half of the available digits, so half of all possible numbers made from these digits will be divisible by 4.

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If the numbers must use each digit exactly once, there will be 4! = 24 of them. 24/2 = 12 of these 4-digit numbers will be divisible by 4.

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