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3 years ago

6

Factor completely 3x^4 - 3x ^3 - 18x ^2. Which of the following is one of the factors?

1 answer:

Otrada [13]3 years ago

7 0

Answer:

$3x^4 - 3x ^3 - 18x ^2=3x^2(x+2)(x-3).$

Step-by-step explanation:

The expression $3x^4 - 3x ^3 - 18x ^2$ consists of three terms:

$3x^4;$
$-3x^3;$
$-18x^2.$

These three terms have common factor $3x^2.$ Thus,

$3x^4 - 3x ^3 - 18x ^2=3x^2(x^2-x-6).$

Consider the expression $x^2-x-6.$ You can rewrite it as

$x^2-x-6=x^2+2x-3x-6=x(x+2)-3(x+2)=(x+2)(x-3).$

The whole expression takes look

$3x^4 - 3x ^3 - 18x ^2=3x^2(x+2)(x-3).$

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In the figure above, PQRS is a circle. If PQT and SRT<br>are straight lines, find the value of x.

Elena L [17]

Given:

PQRS is a circle, PQT and SRT are straight lines.

To find:

The value of x.

Solution:

Since PQRS is a circle, PQT and SRT are straight lines, therefore, PQRS isa cyclic quadrilateral.

We know that, sum of opposite angles of a cyclic quadrilateral is 180 degrees.

$m\angle SPQ+m\angle QRS=180^\circ$

$81^\circ+m\angle QRS=180^\circ$

$m\angle QRS=180^\circ-81^\circ$

$m\angle QRS=99^\circ$

Now, SRT is a straight line.

$m\angle QRT+m\angle QRS=180^\circ$ (Linear pair)

$m\angle QRT+99^\circ=180^\circ$

$m\angle QRT=180^\circ-99^\circ$

$m\angle QRT=81^\circ$ ...(i)

According to the Exterior angle theorem, in a triangle the measure of an exterior angle is equal the sum of the opposite interior angles.

Using exterior angle theorem in triangle QRT, we get

$m\angle PQR=m\angle QRT+m\angle QTR$

$x=81^\circ+22^\circ$

$x=103^\circ$

Therefore, the value of x is 103 degrees.

4 0

3 years ago

Your family drives from Austin Texas to Tampa Florida. The trip is 1145 mi and lasts four days. How many miles should your famil

Colt1911 [192]

286.2...round down soo...286 miles

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3 years ago

Solve the equation 3x-1=x+9

Sever21 [200]

5.

3x - 1 = x + 9

Subtract x on both sides

2x - 1 = 9

Add one on both sides.

2x = 10

Divide by 2 to get the x.

x = 5

Hope this helps!

5 0

3 years ago

Read 2 more answers

A triangle has side lengths of 19 centimetres, 19 centimetres, and 20 centimetres. Is this triangle equilateral?

Sedbober [7]

Answer:

no a equilateral triangle has the same length sides all the way around

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3 years ago

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Svetllana [295]

Answer:

they are both a function

Step-by-step explanation:

because i did this back in 8th grade

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3 years ago