You can factor (x^3 and 6x^2) and (-4x and -24).
So x^2(x+6) - 4(x+6)
(x^2-4)(x+6)
(x-2)(x+2)(x+6)
3cm because if you multiple each one you could divide to
$60. You change 25% to the decimal of .25 and multiply it by $240 to see what 25% of $240 is.
Answer:
x = -6
Step-by-step explanation:
Eliminate
.
![u + v = (3x - 4y) + (x + 4y) = 4x \implies x = \dfrac{u+v}4](https://tex.z-dn.net/?f=u%20%2B%20v%20%3D%20%283x%20-%204y%29%20%2B%20%28x%20%2B%204y%29%20%3D%204x%20%5Cimplies%20x%20%3D%20%5Cdfrac%7Bu%2Bv%7D4)
Eliminate
.
![u - 3v = (3x - 4y) - 3 (x + 4y) = -16y \implies y = \dfrac{3v-u}{16}](https://tex.z-dn.net/?f=u%20-%203v%20%3D%20%283x%20-%204y%29%20-%203%20%28x%20%2B%204y%29%20%3D%20-16y%20%5Cimplies%20y%20%3D%20%5Cdfrac%7B3v-u%7D%7B16%7D)
The Jacobian for this change of coordinates is
![J = \begin{bmatrix} x_u & x_v \\ y_u & y_v \end{bmatrix} = \begin{bmatrix} \dfrac14 & \dfrac14 \\\\ -\dfrac1{16} & \dfrac3{16} \end{bmatrix}](https://tex.z-dn.net/?f=J%20%3D%20%5Cbegin%7Bbmatrix%7D%20x_u%20%26%20x_v%20%5C%5C%20y_u%20%26%20y_v%20%5Cend%7Bbmatrix%7D%20%3D%20%5Cbegin%7Bbmatrix%7D%20%5Cdfrac14%20%26%20%5Cdfrac14%20%5C%5C%5C%5C%20-%5Cdfrac1%7B16%7D%20%26%20%5Cdfrac3%7B16%7D%20%5Cend%7Bbmatrix%7D)
with determinant
![\det(J) = \dfrac14\cdot\dfrac3{16} - \dfrac14\cdot\left(-\dfrac1{16}\right) = \dfrac1{16}](https://tex.z-dn.net/?f=%5Cdet%28J%29%20%3D%20%5Cdfrac14%5Ccdot%5Cdfrac3%7B16%7D%20-%20%5Cdfrac14%5Ccdot%5Cleft%28-%5Cdfrac1%7B16%7D%5Cright%29%20%3D%20%5Cdfrac1%7B16%7D)