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1 year ago

6x³ + 3x how do you factor out the GCF in this question??

Mathematics

2 answers:

shepuryov [24]1 year ago

7 0

Hope this helps, comment if you have any questions:)))

maw [93]1 year ago

4 0

Hi student, let me help you out! :)

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We are asked to factor out the GCF in the expression

$\star~\star\mathrm{6x^3+3x}~\star~\star$

$\triangle~\fbox{\bf{KEY:}}$

Divide every single term of the expression by the GCF (Greatest Common Factor).

So let's divide.

But first. we should work out the GCF.

Both terms have 3x in common, so we divide both terms by 3x:

$\mathrm{6x^3+3x}$

$\mathrm{3x(2x^2+1)}$

To ensure that we've factored correctly, we can always use the distributive property, distribute 3x and see whether or not we end up with $\mathtt{6x^3+3x}$ .

So the answer is

$\mathrm{3x(2x^2+1)}$

Notice I put parentheses around <em>2x²+1</em>. This indicates that 3x is multiplied times both 2x² and 1.

Hope it helps you out! :D

Ask in comments if any queries arise.

#StudyWithBrainly

~Just a smiley person helping fellow students :)

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Someone help me please. I don't just want the answer, I need an explanation on how it's done too.

NARA [144]

Answer:

Below.

Step-by-step explanation:

f) (a + b)^3 - 4(a + b)^2

The (a+ b)^2 can be taken out to give:

= (a + b)^2(a + b - 4)

= (a + b)(a + b)(a + b - 4).

g) 3x(x - y) - 6(-x + y)

= 3x( x - y) + 6(x - y)

= (3x + 6)(x - y)

= 3(x + 2)(x - y).

h) (6a - 5b)(c - d) + (3a + 4b)(d - c)

= (6a - 5b)(c - d) + (-3a - 4b)(c - d)

= -(c - d)(6a - 5b)(3a + 4b).

i) -3d(-9a - 2b) + 2c (9a + 2b)

= 3d(9a + 2b) + 2c (9a + 2b)

= 3d(9a + 2b) + 2c (9a + 2b).

= (3d + 2c)(9a + 2b).

j) a^2b^3(2a + 1) - 6ab^2(-1 - 2a)

= a^2b^3(2a + 1) + 6ab^2(2a + 1)

= (2a + 1)( a^2b^3 + 6ab^2)

The GCF of a^2b^3 and 6ab^2 is ab^2, so we have:

(2a + 1)ab^2(ab + 6)

= ab^2(ab + 6)(2a + 1).

4 0

2 years ago

Plz show your work. Thx!! <br> 9m=6

grandymaker [24]

So first you would divide the 9 on both sides then 6 divided by 9 would be .6 repeating so m=.6 repeating.

5 0

2 years ago

Determine whether the function f(x)= 1/x^2 is even, odd or neither.

gulaghasi [49]

The function f(x)= 1/x^2 is even. Hope that helps!

4 0

2 years ago

Given gif and GHF, write three proportions involving geometric mean.<br>

almond37 [142]

Answer:

$\frac{z}{h}=\frac{h}{y}\\\\\frac{a}{x}=\frac{x}{z}\\\\\frac{a}{w}=\frac{w}{y}$

Step-by-step explanation:

For this exercise it is important to remember that a Right triangle is a triangle that has an angle that measures 90 degrees.

According to the Altitude Rule, given a Right triangle, if you draw an altitude from the vertex of the angle that measures 90 degrees (The right angle) to the hypotenuse, the measure of that altitude is the geometric mean between the measures of the two segments of the hypotenuse.

In this case, you can identify that the altitude that goes from the vertex of the right angle ( $\angle G=90\°$ ) to the hypotenuse of the triangle, is:

$GF=h$

Then, based on the Altitude Rule, you can set up the following proportion:

$\frac{z}{h}=\frac{h}{y}$

According to the Leg Rule, each leg is the mean proportional between the hypotenuse and the portion of the hypotenuse that is located directly below that leg of the triangle.

Knowing this, you can set up the following proportions:

$\frac{a}{x}=\frac{x}{z}\\\\\frac{a}{w}=\frac{w}{y}$

6 0

2 years ago

Read 2 more answers

The distance on the map between Yappy city and Quiet city is 23 cm.

jekas [21]

The actual distance between Yappy city and Quiet city when it is 23 cm in map is 9.2 miles.

What is scaling ?

It is the technique to resize drawing with comparing to actual size of object which uses proportion or ratio. For example, Mapping of earth, drawing prototype of automobiles.

It is given that :

The distance on the map between Yappy city and Quiet city is 23 cm

and,

5cm = 2 miles

now, for 1 cm on map it is equal to 2/5 miles of actual distance.

Therefore to find the actual distance of 23 cm in map we simply multiply 23 with 2/5 :

actual distance :

2/5 x 23 = 9.2 miles

Therefore, the actual distance between Yappy city and Quiet city is 9.2 miles.