2/3x+2= 2 1/3n<br> A. 0<br> B. 1/2<br> C. -2<br> D. 2

Describe the steps you would use to factor 2x3 + 5x2 – 8x – 20 completely. Then state the factored form.

WARRIOR [948]

The polynomial $2x^3 + 5x^2-8x-20$ may have solutions which are the divisors of -20, therefore -20 has the following divisors: $\pm 1, \pm 2, \pm 4, \pm 5, \pm 10, \pm 20$ .
If x=1, then $2\cdot1^3 + 5\cdot1^2-8\cdot1-20=-20\neq 0$ ,
if x=-1, then $2\cdot(-1)^3 + 5\cdot(-1)^2-8\cdot(-1)-20=-9\neq 0$ ,
if x=2, then $2\cdot2^3 + 5\cdot2^2-8\cdot2-20=0$ , then x=2 is a solution and you have the first factor (x-2).
If x=-2, then $2\cdot(-2)^3 + 5\cdot(-2)^2-8\cdot(-2)-20=0$ , then x=-2 is a solution, so you have the second factor (x+2).
Since x-2 and x+2 are two factors of $2x^3 + 5x^2-8x-20$ , then the polynomial $x^2-4$ is a divisor of $2x^3 + 5x^2-8x-20$ and dividing the polynomial $2x^3 + 5x^2-8x-20$ by $x^2-4$ you obtain
$2x^3 + 5x^2-8x-20=(x-2)(x+2)(2x+5)$ .

5 0

3 years ago

Read 2 more answers

Help

BigorU [14]

Answer:

$69$

thats it all of them are 69

4 0

3 years ago

The ratio of dogs to cats at a pet store is 11: 4. If there are 90 total pets (dogs and cats), how many cats are there?

swat32

Answer:

number of cats

$90 \times \frac{4}{15} \\ 24cats$

5 0

3 years ago

If u+v+w=0, show that u x v = v x w = w x u.

Flauer [41]

Take the cross product of both sides of $\mathbf u+\mathbf v+\mathbf w=\mathbf0$ with $\mathbf u,\mathbf v,\mathbf w$ to generate a system of three simultaneous equations.

$(\mathbf u+\mathbf v+\mathbf w)\times\left\{\begin{matrix}\mathbf u\\\mathbf v\\\mathbf w\end{matrix}\right\}=\mathbf0\times\left\{\begin{matrix}\mathbf u\\\mathbf v\\\mathbf w\end{matrix}\right\}$
$\implies\begin{cases}\mathbf u\times\mathbf u+\mathbf u\times\mathbf v+\mathbf u\times\mathbf w=\mathbf0\\\mathbf v\times\mathbf u+\mathbf v\times\mathbf v+\mathbf v\times\mathbf w=\mathbf0\\\mathbf w\times\mathbf u+\mathbf w\times\mathbf v+\mathbf w\times\mathbf w=\mathbf0\end{cases}$
$\implies\begin{cases}\mathbf u\times\mathbf v+\mathbf u\times\mathbf w=\mathbf0\\\mathbf v\times\mathbf u+\mathbf v\times\mathbf w=\mathbf0\\\mathbf w\times\mathbf u+\mathbf w\times\mathbf v=\mathbf0\end{cases}$

since $\mathbf x\times\mathbf x=\mathbf0$ for any vector $\mathbf x$ .

Finally, use the fact that the cross product is anticommutative, i.e. $\mathbf x\times\mathbf y=-\mathbf y\times\mathbf x$ . The conclusion follows.

4 0

4 years ago

8(2x- 6)= 96 solve for x

9966 [12]

Answer:

x=9

Step-by-step explanation:

To solve, simplify the equation them isolate x.

8(2x- 6) = 96 Distribute over brackets by multiplying

16x - 48 = 96 Add 48 to both sides

16x = 144 Divide both sides by 16

x = 9 Final answer

5 0

3 years ago

2/3x+2= 2 1/3n A. 0 B. 1/2 C. -2 D. 2