Factor completely. - 2x² + 20x – 48 = What is the missing factor?

Mathematics

2 answers:

docker41 [41]3 years ago

6 0

2x(-X+12)—4(x-12) where the roots/answers are 4 and 6

Lemur [1.5K]3 years ago

4 0

Answer:

- 2(x - 6)(x - 4)

Step-by-step explanation:

Given

- 2x² + 20x - 48 ← factor out - 2 from each term

= - 2 (x² - 10x + 24) ← factor the quadratic

Consider the factors of the constant term (+ 24) which sum to give the coefficient of the x- term (- 10)

The factors are - 6 and - 4, since

- 6 × - 4 = + 24 and - 6 - 4 = - 10, thus

x² - 10x + 24 = (x - 6)x - 4) and

- 2x² + 20x - 48 = - 2 (x - 6)(x - 4) ← in factored form

You might be interested in

True or False:<br> The following system of equations is consistent.

vampirchik [111]

A system of equation is consistent if there is at least one solution. Since this system of equations has a single solution, it is consistent, the answer is true.

6 0

4 years ago

Use cylindrical coordinates. find the volume of the solid that lies within both the cylinder x2 y2 = 9 and the sphere x2 y2 z2 =

marissa [1.9K]

In Cartesian coordinates, the region is given by $-3\le x\le3$ , $-\sqrt{9-x^2}\le y\le\sqrt{9-x^2}$ , and $-\sqrt{16-x^2-y^2}\le z\le\sqrt{16-x^2-y^2}$ . Converting to cylindrical coordinates, using

$\begin{cases}\mathbf x(r,\theta,\zeta)=r\cos\theta\\\mathbf y(r,\theta,\zeta)=r\sin\theta\\\mathbf z(r,\theta,\zeta)=\zeta\end{cases}$

we get a Jacobian determinant of $r$ , and the region is given in cylindrical coordinates by $0\le\theta\le2\pi$ , $0\le r\le3$ , and $-\sqrt{16-r^2}\le z\le\sqrt{16-r^2}$ .

The volume is then

$\displaystyle\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=3}\int_{z=-\sqrt{16-r^2}}^{z=\sqrt{16-r^2}}r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta=\dfrac{4(64-7\sqrt7)\pi}3$