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alisha [4.7K]
2 years ago
15

Factor the polynomial as a product of linear factors with complex coefficients.

Mathematics
2 answers:
lys-0071 [83]2 years ago
8 0

15386553sssssssssssssssssssssssssssssssssssssssss

shepuryov [24]2 years ago
3 0

Answer:

The function

f(x) = x3 + 2x2 − x − 2

is a trinomial and it is expected that it has three factors corresponding to the three roots. The possible roots could 1, -1, 2, or -2. Trying out 1

f(1) = 1 + 2 - 1 - 2 = 0

According to the remainder theorem (x - 1) is a factor. By doing synthetic division

1 | 1 2 -1 -2

      1  3  2

    1  3 2  0

f(x) = (x - 1)(x2 + 3x + 2)

which can further be factored into

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

The three factors are

x-1

x+1

x+2

which are all linear expressions

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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12/2 = 6

12 and 6 are on the same side in both triangles , that is why I used those two numbers to figure out the scale factor

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2. Which number is a solution of the inequality? <br> -5 <br> -6<br> 6<br> 7
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3 years ago
Read 2 more answers
This is the pond in a shape of a prism, it is completely full of water. Colin uses a pump to empty the pond. The level goes down
AnnZ [28]

Answer:

150 minutes

Step-by-step explanation:

P.S - The exact question is -

Given - This is the pond in a shape of a prism, it is completely full of

             water. Colin uses a pump to empty the pond. The level goes

             down by 20 cm in the first 30 min.

To find - Work put how many minutes Colin has to wait for the pond

               to completely empty.

Proof -

Given that,

Height of prism = 1 m

Also,

Base of the prism is trapezium and

Sides of the trapezium are 0.6 m and 1.4 m

Height of trapezium is 2 m

We know that,

Area of trapezium = \frac{1}{2}× (sum of sides)× height

                             =  \frac{1}{2}× (0.6 + 1.4)× 2

                             =  \frac{1}{2}× (2)× 2

                             =  2 m²

⇒Area of trapezium = 2 m²

Now,

Volume of prism = Area of trapezium × height of prism

                          = 2 m² × 1 m

                          = 2 m³

⇒Volume of prism = 2 m³

Now,

Given that the level goes down by 20 cm in the first 30 min

We know

100 cm = 1 m

⇒1 cm = \frac{1}{100} m = 0.01 m

⇒20 cm = 20×0.01 m = 0.2 m

⇒The level goes down by 0.2 m in the first 30 min.

Also,

we know that height of water = height of prism = 1 m

So, the remaining water left in the pond = 1 m - 0.2 m = 0.8 m

Also,

Volume of Remaining water = Area of trapezium × height

                                           = 2 m² × 0.8 m

                                           = 1.6 m³

⇒Volume of Remaining water = 1.6 m³

Now,

Volume of emptied water = Total Volume - Volume of Remaining water

                                       = 2 m³ - 1.6 m³

                                       = 0.4 m³

⇒Volume of emptied water = 0.4 m³

Now,

0.4 m³ water will be empty in 30 minutes

⇒ 1 m³ water will be empty in \frac{30}{0.4} = 75 minutes

⇒1.6 m³ water will be empty in 1.6 × 75 = 120 minutes

∴ we get

The remaining water is empty in 120 minutes

So,

Total pond is empty in 120 + 30 minutes

⇒Total pond is empty in 150 minutes

5 0
2 years ago
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