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3 years ago

What is the completely factored form of this polynomial? 18x^3 – 120x^2 – 42x

Mathematics

2 answers:

Nookie1986 [14]3 years ago

8 0

The completely factored form is 6x(3x+1)(x-7)

lyudmila [28]3 years ago

4 0

Answer:

6x(3x + 1)(x - 7) .

Step-by-step explanation:

First look for the greatest common factor of the 3 terms.

It is 6x, so

18x^3 – 120x^2 – 42x

= 6x(3x^2 - 20x - 7)

Now we look to factor the quadratic expression in the parentheses:

Use the 'ac' method:

The first and last coefficients are multiplied

3 * -7 = -21.

We look for 2 numbers whose product is -21 and whose sum is -20:

They are -21 and + 1 , so we write:

6x(3x^2 - 21x + 1x - 7)

= 6x [ (3x(x - 7) + 1(x - 7)] Note that x - 7 is common, so:

= 6x(3x + 1)(x - 7) Answer

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Write the equation of a parabola having the vertex (1, −2) and containing the point (3, 6) in vertex form. Then, rewrite the equ

In-s [12.5K]

PART A

The equation of the parabola in vertex form is given by the formula,

$y - k = a {(x - h)}^{2}$

where

$(h,k)=(1,-2)$

is the vertex of the parabola.

We substitute these values to obtain,

$y + 2 = a {(x - 1)}^{2}$

The point, (3,6) lies on the parabola.

It must therefore satisfy its equation.

$6 + 2 = a {(3 - 1)}^{2}$

$8= a {(2)}^{2}$

$8=4a$

$a = 2$
Hence the equation of the parabola in vertex form is

$y + 2 = 2 {(x - 1)}^{2}$

PART B

To obtain the equation of the parabola in standard form, we expand the vertex form of the equation.

$y + 2 = 2{(x - 1)}^{2}$

This implies that

$y + 2 = 2(x - 1)(x - 1)$

We expand to obtain,

$y + 2 = 2( {x}^{2} - 2x + 1)$

This will give us,

$y + 2 = 2 {x}^{2} - 4x + 2$

$y = {x}^{2} - 4x$

This equation is now in the form,

$y = a {x}^{2} + bx + c$
where

$a=1,b=-4,c=0$

This is the standard form

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3 years ago

Simplify (6g4h5)2<br> What is the answer

SVETLANKA909090 [29]

Answer:

12g8h10

Multiply each variable quantity by 2 and combine.

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3 years ago

Solve the equation for all values of x by completing the square.<br> x^2 + 4x = 32

Black_prince [1.1K]

Answer:

x^2+4x-32=0

(mid-term breaking---4 x 8=32)

x^2+8x-4x-32=0

x(x+8)-4(x+8)

x+8=0 or x-4=0

So x=+4 or x=-8

Step-by-step explanation:

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3 years ago

Best and correct answer gets brainliest!!!

dmitriy555 [2]

59 degrees!
because you set up your problem: 3c+2+2c-7=90
then combine all like terms: 5c-5=90
Add 5 to both sides: 5c=95
then divide both sides by 5: c=19
Plug in your answer: 3(19)+2=59

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3 years ago

2. Which expression is equivalent to 2x2 + (4x - 6x2)+9 - (6x + 3)?

frez [133]

The answer is g you just have to combine the Like terms

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3 years ago