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3 years ago

What is the greatest common factor of the polynomial expression 2x^3 - 4x^2 + 6x?

Mathematics

1 answer:

iren2701 [21]3 years ago

5 0

Step-by-step explanation:

$2 {x}^{3} - 4 {x}^{2} + 6x \\ = 2x( {x}^{2} - 2x + 3) \\ \because \: 2x \: is \: common \: from \: all \: terms \\ \therefore \: greatest \: common \: factor = 2x$

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Complete the square to transform the quadratic equation into the form (x – p)2 = q. x2 - 12x - 5 = 7 A) (x - 36)2 = 9 B) (x - 6)

iren2701 [21]

x2 - 12x - 12 = 0

(x - 6)2 - 48 = 0

(x - 6)2 = 48

Hence, the answer is (B).

6 0

3 years ago

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The length of each side of an equilateral triangle is increased by 20%, resulting in triangle ABC. If the length of each side of

kompoz [17]

Answer: Area of ΔABC is 2.25x the area of ΔDEF.

Step-by-step explanation: Because equilateral triangle has 3 equal sides, area is calculated as

$A=\frac{\sqrt{3} }{4} a^{2}$

with a as side of the triangle.

Triangle ABC is 20% bigger than the original, which means its side (a₁) measures, compared to the original:

a₁ = 1.2a

Then, its area is

$A_{1}=\frac{\sqrt{3} }{4}(1.2a)^{2}$

$A_{1}=\frac{\sqrt{3} }{4}1.44a^{2}$

Triangle DEF is 20% smaller than the original, which means its side is:

a₂ = 0.8a

So, area is

$A_{2}=\frac{\sqrt{3} }{4} (0.8a)^{2}$

$A_{2}=\frac{\sqrt{3} }{4} 0.64a^{2}$

Now, comparing areas:

$\frac{A_{1}}{A_{2}}= (\frac{\sqrt{3}.1.44a^{2} }{4})(\frac{4}{\sqrt{3}.0.64a^{2} } )$

$\frac{A_{1}}{A_{2}} =$ 2.25

The area of ΔABC is 2.25x greater than the area of ΔDEF.

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2 years ago

What is the completely factored form of f(x)=x3+5x2+4x−6?

Gre4nikov [31]

$f(x)=x^3+5x^2+4x-6$
$f(-3)=(-3)^3+5(-3)^2+4(-3)-6=0\implies x+3\text{ is a factor of }f(x)$

Synthetic division yields

-3 | 1   5   4   -6
.    |      -3 -6    6
- - - - - - - - - - - - -
.    | 1   2 -2    0

which translates to

$\dfrac{x^3+5x^2+4x-6}{x+3}=x^2+2x-2$

with remainder 0. Now by the quadratic formula,

$x^2+2x-2=0\implies x=\dfrac{-2\pm\sqrt{2^2-4(1)(-2)}}2=-1\pm\sqrt3$

and so

$f(x)=x^3+5x^2+4x-6=(x+3)(x-(-1+\sqrt3))(x-(-1-\sqrt3))$

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3 years ago

Five and one third times twenty eight

hoa [83]

149.333333333... is your answer

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3 years ago

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What is 12/13 times 10/11

vitfil [10]

120/143. 12 x 10 is 120, and 13 x 11 is 143. It is already in simplest form.

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2 years ago

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