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3 years ago

Multiply (3x-7)(2x^2-8x+3)

Mathematics

1 answer:

xxTIMURxx [149]3 years ago

4 0

Answer:

6x^3-38x^2+65x-21

Step-by-step explanation:

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What are the solutions of the equation x6 + 6x3 + 5 = 0? Use factoring to solve.

lapo4ka [179]

Consider the equation $x^6+6x^3+5=0$ .

First, you can use the substitution $t=x^3$ , then $x^6=(x^3)^2=t^2$ and equation becomes $t^2+6t+5=0$ . This equation is quadratic, so

$D=6^2-4\cdot 5\cdot 1=36-20=16=4^2,\ \sqrt{D}=4,\\ \\ t_{1,2}=\dfrac{-6\pm 4}{2} =-5,-1$ .

Then you can factor this equation:

$(t+5)(t+1)=0$ .

Use the made substitution again:

$(x^3+5)(x^3+1)=0$ .

You have in each brackets the expression like $a^3+b^3$ that is equal to $(a+b)(a^2-ab+b^2)$ . Thus,

$x^3+5=(x+\sqrt[3]{5})(x^2-\sqrt[3]{5}x+\sqrt[3]{25}) ,\\x^3+1=(x+1)(x^2-x+1)$

and the equation is

$(x+\sqrt[3]{5})(x^2-\sqrt[3]{5}x+\sqrt[3]{25})(x+1)(x^2-x+1)=0$ .

Here $x_1=-\sqrt[3]{5} , x_2=-1$ and you can sheck whether quadratic trinomials have real roots:

1. $D_1=(-\sqrt[3]{5}) ^2-4\cdot \sqrt[3]{25}=\sqrt[3]{25} -4\sqrt[3]{25} =-3\sqrt[3]{25}$ .

2. $D_2=(-1)^2-4\cdot 1=1-4=-3$ .

This means that quadratic trinomials don't have real roots.

Answer: $x_1=-\sqrt[3]{5} , x_2=-1$

If you need complex roots, then

$x_{3,4}=\dfrac{\sqrt[3]{5}\pm i\sqrt{3\sqrt[3]{25}}}{2} ,\\ \\x_{5,6}=\dfrac{1\pm i\sqrt{3}}{2}$ .

6 0

3 years ago

Pls pls help it's really urgent!!!

Ierofanga [76]

None of the above

i think sorry if is wrong

4 0

3 years ago

Can someone pls give answer to number 4

katen-ka-za [31]

Step-by-step explanation:

Supplement= 180°- 13°

167° Answer

3 0

2 years ago

Read 2 more answers

All planets revolve around thensun in elliptical orbits. Uranus's furthest distance from the sun is approximately 3.004 x 10 km,

boyakko [2]

Add the two numbers 3004000000+2749000000 and divide by 2
which equals 2876500000 or 2.8765x10^9

5 0

3 years ago

Todd uses 21 white tiles & some black tiles to make a mosaic.The mosaic has a total area of 144 square centimeters.Each tile

icang [17]

Answer: Todd used 27 black tiles.

Step-by-step explanation:

Let x represent the number of black tiles that Todd used.

Todd uses 21 white tiles & some black tiles to make a mosaic. This means that the total number of white and black tiles that Todd used is 21 + x

Each tile has an area of 3 square centimeters. This means that the total area covered by the white tiles is

21 × 3 = 63 square centimeters

Also, the total area covered by the black tiles is

3 × x = 3x square centimeters

The mosaic has a total area of 144 square centimeters. This means that

3x + 63 = 144

3x = 144 - 63

3x = 81

x = 81/3 = 27

3 0

3 years ago