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3 years ago

Factor using any method: 8x^3-12^2-2x+3

Mathematics

2 answers:

sveticcg [70]3 years ago

7 0

8x^3-2x^2-2x+3
=4x^3 x （2x-3）-（2x-3）
=（4x^2-1） x（2x-3）
=（2x-1）x（2x+1）x（2x-3）

neonofarm [45]3 years ago

4 0

Regroup: (8x^3-12x^2)-(2x-3)
4x^2(2x-3)-(2x-3)
(2x-3)(4x^2-1)
(2x-3)(2x+1)(2x-1)

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Solve the system of equations by finding the reduced row echelon form of the augmented matrix. Write the solutions for x and y i

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Answer:

The solutions for the given system of equations are:

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Step-by-step explanation:

Given the equation system:

$\left \{ {{3x+y+4z=-3} \atop {-x+y+4z=17}} \right.$

We obtain the following matrix:

$\left[\begin{array}{cccc}3&1&4&-3\\-1&1&4&17\end{array}\right]$

Step 1: Multiply the fisrt row by 1/3.

$\left[\begin{array}{cccc}1&\frac{1}{3} &\frac{4}{3}&-1\\-1&1&4&17\end{array}\right]$

Step 2: Sum the first row and the second row.

$\left[\begin{array}{cccc}1&\frac{1}{3} &\frac{4}{3}&-1\\0&\frac{4}{3} &\frac{16}{3}&16\end{array}\right]$

Step 3: Multiply the second row by 3/4.

$\left[\begin{array}{cccc}1&\frac{1}{3} &\frac{4}{3}&-1\\0&1 &4&12\end{array}\right]$

Step 4: Multiply the second row by -1/3 and sum the the first row.

$\left[\begin{array}{cccc}1&0 &0&-5\\0&1 &4&12\end{array}\right]$

The result of the reduced matrix is:

$\left \{ {{x=-5} \atop {y+4z=12}} \right.$

This is equal to:

$\left \{ {{x=-5} \atop {y=12-4z}} \right.$

These are the solutions for the system of equations in terms of z, where z can be any number.

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