(x^3-2x^2-75) divided by (x-5)

Mathematics

1 answer:

Olin [163]3 years ago

3 0

Hello!

$\large\boxed{x^{2} + 3x + 15}$

To solve, we can use polynomial long division:

Set up the process using (x³ - 2x² - 75) as the dividend. Put in a place holder of (0x) to ensure that a proper answer is reached.

Use (x - 5) as the divisor.

Steps for dividing:

1. Find how many times that the first term in the divisor will go into the first term of the dividend. In the first step, (x - 5) goes into (x³ - 2x²) x² times. Put this at the top for our quotient .

2. Multiply both of the terms in the divisor by x². Put those expressions underneath the dividend and subtract.

3. Bring down the next number in the dividend and find how many times (x - 5) goes into 3x² + 0x. We get 3x times, so repeat the same steps above.

4. Continue until you finish with the last two numbers. If the remainder is 0, your solution is simply the quotient at the top. (In this instance).

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Last year , there were 30 male members and 20 female members in a Chess Club . This year , the number of male members is decreas

LekaFEV [45]

The r% of a quantity x is computed by dividing x in 100 parts, and considering r of such parts. So, the r% of the male is

$30\times\cfrac{r}{100} = 0.3 r$

and similarly, the r% of female is

$20\times\cfrac{r}{100} = 0.2 r$

The number of males decreased by this quantity, so now it is

$30 - 0.3r$

and the number of female increased by this quantity, so now it is

$20+0.2r$

we know that these two new counts are the same number, so we can build and solve the equality

$30 - 0.3r = 20+0.2r$

Subtract 20 and add 0.3r from both sides:

$10 = 0.5r$

Divide both sides by 0.5 to solve for r:

$r = 20$

Let's check the answer

The 20% of 30 is $30 \times \frac{20}{100} = 6$ , while the 20% of 20 is 4. So, we are stating that $30-6 = 20+4$ which is true because both expressions evaluate to 24.