Factor completely 3x^5-75x^3=

Mathematics

1 answer:

KiRa [710]3 years ago

7 0

Answer:

$\huge\boxed{3x^5-75x^3=3x^3(x-5)(x+5)}$

Step-by-step explanation:

$3x^5=3\cdot x^{3+2}=3\cdot x^3\cdot x^2=\boxed{3x^3}\cdot x^2\\\\75x^3=25\cdot\boxed{3x^3}\\\\3x^5-75x^3=3x^3(x^2-25)=3x^3(x^2-5^2)\\\\\text{Use}\ a^2-b^2=(a-b)(a+b)\\\\=3x^3(x-5)(x+5)$

You might be interested in

16) Please help with question. WILL MARK BRAINLIEST + 10 POINTS.

Katyanochek1 [597]

We will use the sine and cosine of the sum of two angles, the sine and consine of $\frac{\pi}{2}$ , and the relation of the tangent with the sine and cosine:

$\sin (\alpha+\beta)=\sin \alpha\cdot\cos\beta + \cos\alpha\cdot\sin\beta

\cos(\alpha+\beta)=\cos\alpha\cdot\cos\beta-\sin\alpha\cdot\sin\beta$

$\sin\dfrac{\pi}{2}=1,\ \cos\dfrac{\pi}{2}=0$

$\tan\alpha = \dfrac{\sin\alpha}{\cos\alpha}$

If you use those identities, for $\alpha=x,\ \beta=\dfrac{\pi}{2}$ , you get:

$\sin\left(x+\dfrac{\pi}{2}\right) = \sin x\cdot\cos\dfrac{\pi}{2} + \cos x\cdot\sin\dfrac{\pi}{2} = \sin x\cdot0 + \cos x \cdot 1 = \cos x$

$\cos\left(x+\dfrac{\pi}{2}\right) = \cos x \cdot \cos\dfrac{\pi}{2} - \sin x\cdot\sin\dfrac{\pi}{2} = \cos x \cdot 0 - \sin x \cdot 1 = -\sin x$

Hence:

$\tan \left(x+\dfrac{\pi}{2}\right) = \dfrac{\sin\left(x+\dfrac{\pi}{2}\right)}{\cos\left(x+\dfrac{\pi}{2}\right)} = \dfrac{\cos x}{-\sin x} = -\cot x$

3 0

3 years ago

Help please. 10 POINTS

Verdich [7]

Answer:

$(6^{10})^{-7}$

Step-by-step explanation:

5 0

3 years ago

L.B Jhonson middle school held a track and field event during the school year. The chess club sold various drink and snack items

forsale [732]

Answer:

$5.50

Step-by-step explanation:

you start by taking 2673 and then you have to divide that 486 and when you do that you get 5.5. Since that question states that each club sold each item for the same price then each item was sold for five dollars and fifty cents.

6 0

3 years ago

Barry buys a package of pasta for $2.39 and a jar of tomato sauce for $3.09. He uses a $0.75 coupon and a $0.50 coupon.

seraphim [82]

Answer:$4.23

Step-by-step explanation:

6 0

3 years ago

What is the inverse of the function f(x) = 2x – 10?

Lana71 [14]

Answer:

$h(x)=\dfrac{x}{2}+5$