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3 years ago

Factor 3x^3+6x^2+x+2 by grouping

Mathematics

2 answers:

bezimeni [28]3 years ago

7 0

The answer for this question when grouping:

(x+2)(3x^2+1)

UkoKoshka [18]3 years ago

7 0

3x^3 + 6x^2 + x +2

Let's divide the question into the left and right side:
The left side:
3x^3 + 6x^2
Take out the greatest common factor (3x^2)
3x^2(x+2)

Now the right side:
x+2
Take out greatest common factor (1)
1(x+2)

Notice how each side has a parenthesis of (x + 2); this is good. We combine the matching elements into one, and take the greatest common factors we pulled and make them into a group. As shown:

(3x^2 +1) is the two greatest common factors we pulled.

(x+2) is the common parenthesis.
Now combine them for your answer:

(3x^2+1)(x+2) is your factored answer.

I hope this Helps!

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Given the function f(x) = 4(2)x, Section A is from x = 1 to x = 2 and Section B is from x = 3 to x = 4.

Dmitry [639]

Answer:

Step-by-step explanation:

I'm sure you want your functions to appear as perfectly formed as possible so that others can help you. f(x) = 4(2)x should be written with the " ^ " sign to denote exponentation: f(x) = 4(2)^x

f(b) - f(a)

The formula for "average rate of change" is a.r.c. = --------------

b - a

change in function value

This is equivalent to ---------------------------------------

change in x value

For Section A: x changes from 1 to 2 and the function changes from 4(2)^1 to 4(2)^2: 8 to 16. Thus, "change in function value" is 8 for a 1-unit change in x from 1 to 2. Thus, in this Section, the a.r.c. is:

------ = 8 units (Section A)

Section B: x changes from 3 to 4, a net change of 1 unit: f(x) changes from

4(2)^3 to 4(2)^4, or 32 to 256, a net change of 224 units. Thus, the a.r.c. is

224 units

----------------- = 224 units (Section B)

1 unit

The a.r.c for Section B is 28 times greater than the a.r.c. for Section A.

This change in outcome is so great because the function f(x) is an exponential function; as x increases in unit steps, the function increases much faster (we say "exponentially").

7 0

3 years ago

Which are true or false

Savatey [412]

we are given

$y=19.75x$

Here,

y is the number of gallons of water in the pool

x is the number of minutes the truck has been filing the pool

now, we will verify each options

option-A:

When x=1

then y=19.75

so, for 1 minute , number gallons =19.75

so, this is FALSE

option-B:

Since, we have

$y=19.75x$

It is similar to equation of line

y=mx+b

But b=0

It means that it passes through origin

so, this is TRUE

option-C:

$y=19.75x$

we can compare it with

y=mx

where m is the rate

so, we get

$m=19.75$

while we are given

the water in swimming pool increase about 100 gallons by every 5 minutes

so, we get rate as

$m=\frac{100}{5} =20$ gallons per minute

this is close to 19.75

so, they are approximately equal

so, this is TRUE

option-d:

x-value and y-value will show relationship

and ratio will always be constant or equivalent

because it has linear relationship

so, this is TRUE

option-e:

We need to check

(8,150) ..so, x=8 and y=150

we can plug this in our equation

and we get

$150=19.75\times 8$

$150=158$

Since, left side is not equal to right side

so, this can not be point

so, this is FALSE

5 0

3 years ago

How can i simplify 16m cubed -10m squared

adoni [48]

16m cubed - 10m squared......
take out the common factors
they both have a two that can go into it and both have two m's you can take out
so then it becomes
2m squared(8m-5) and thats your answer (:

5 0

3 years ago

Read 2 more answers

Divide (5x + 6x^3 - 8) ÷(x - 2) PLEASE HELP DUE IN 5 MINUTES

Leya [2.2K]

Answer:

6x^2+12x+29+50/x-2

Step-by-step explanation:

3 0

3 years ago

How many variable terms are in the expression 3x3y + 5x2 − 4y + z + 9? (Input a numeric value only.)

Anarel [89]

Answer:

Step-by-step explanation:

A variable term is a mathematical term in which a variable is by itself or is connected to a coefficient(s).

3x3y, 5x2, −4y, z.

7 0

2 years ago