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Dominik [7]
2 years ago
12

Find the polynomial function in standard form that has the zeros listed. 1(multiplicity 2), -2(multiplicity 3)​

Mathematics
1 answer:
finlep [7]2 years ago
5 0

Answer:

  f(x) = x⁵ +4x⁴ +x³ -10x² -4x+8

Step-by-step explanation:

If p is a zero, then (x -p) is a factor. The multiplicity of the zero tells you how many times that is a factor (its exponent).

  f(x) = (x -1)²(x +2)³ = (x² -2x +1)(x³ +6x² +12x +8)

  f(x) = x⁵ +4x⁴ +x³ -10x² -4x+8

_____

<em>Additional comment</em>

You can use the distributive property to write out the 12 terms of the product of the two expanded factors, or you can do a little mental arithmetic based on what you know about the exponent of a product term. (It is the sum of the exponents of its factors.)

The mental exercise can be made easier by writing the coefficients of the factors as though they were two cubics. It works well to write them in two rows:

  \left[\begin{array}{cccc}0&1&-2&1\\1&6&12&8\end{array}\right]

The columns are in order of decreasing powers of x. A relatively simple and symmetrical pattern of sums of cross products is used to find the coefficients of the final polynomial. Working in order of decreasing exponents, we have ...

coefficient of x^6 = (0)(1) = 0

coefficient of x^5 = (0)(6) +(1)(1) = 1

coefficient of x^4 = (0)(12) +(1)(-2) +(1)(6) = 4

coefficient of x^3 = (0)(8) +(1)(1) +(1)(12) +(6)(-2) = 1

coefficient of x^2 = (1)(8) +(6)(1) +(-2)(12) = -10

coefficient of x^1 = (-2)(8) +(12)(1) = -4

coefficient of x^0 = (1)(8) = 8

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Assume that all triangles have interior angles less than 90°.A surveyor sights on a survey marker that is 132.3m distant. She ne
Vadim26 [7]

Answer:

  85.9 m

Step-by-step explanation:

The law of sines can help figure this.

The remaining angle in the triangle is ...

  180° -75° -68° = 37°

This is the angle opposite the leg from the surveyor to the second marker. Referencing the attachment, we have ...

  b/sin(B) = c/sin(C)

  b = sin(B)·c/sin(C) = 132.3·sin(37°)/sin(68°) ≈ 85.873 . . . meters

The surveyor is about 85.9 meters from the second marker.

4 0
3 years ago
A gallon of stain is enough to cover 200 square feet of decking. Bradley has two areas of decking he would like to cover with st
Pani-rosa [81]

The expression that we need to get is:

N = \frac{(23)*(10.4) + (10.5)*(7.2)}{200}

So the correct option is the second one.

<h3>Which expression gives the number of gallons of stain Bradley will need?</h3>

We know that 1 gallon is enough to cover 200 ft².

We have two rectangular areas, one of:

23 feet by 10.4 feet, and other of 10.5 feet by 7.2 feet.

Then the total area is:

A = (23 ft)*(10.4 ft) + (10.5ft)*(7.2 ft)

The number of gallons needed is given by the quotient between the area that we want to cover, and the area that covers one gallon, so the expression is:

N = \frac{(23ft)*(10.4ft) + (10.5ft)*(7.2ft)}{200ft^2} \\\\N = \frac{(23)*(10.4) + (10.5)*(7.2)}{200}

So the corerect option is the second one.

If you want to learn more about algebraic expressions:

brainly.com/question/4344214

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7 0
2 years ago
Step by step what is 3 (x+2)+5x
lesya692 [45]

Answer:

8x+6

Step-by-step explanation:

To simplify it, the first thing you want to do is distribute the three.


So

3(x+2) = 3x+6,

So we can then add the 5x to it.

3x+6+5x

Then, Combine Like Terms

8x+6

6 0
3 years ago
A stadiums parking lot can accommodate 5,000 vehicles. If 35% of the 75,000 fans drive to tonight’s game with two fans per car h
geniusboy [140]

Answer:

35 percent of the 75,000 fans is: 0.35*75,000 = 26,250

since there are 2 fans per car we find the number of cars by dividing 26,250 by 2:

26,250 : 2 = 13,125 cars

5,000 will park at the stadium's parking lots, while the rest 13,125 - 5,000 = 8,125 cars will par at satellite lots.

OR

35% of 75000 = 26250

2 fans in a car

So, = 26250/2

= 13125

Total handling space = 5000

13125 - 5000 = 8125

Step-by-step explanation:

5 0
3 years ago
5(x + 3) represents the area of the rectangle above. Which expression below is
vitfil [10]

Answer: 1,2,3 becuase they are all equivalent its just logic when you think abt it

Step-by-step explanation: 4 makes no sense

3 0
3 years ago
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