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3 years ago

What is the product? 3x^5 (2x^2+4x+1)

Mathematics

2 answers:

s2008m [1.1K]3 years ago

8 0

Answer:

The product of the given polynomial $3x^5(2 x^2+4x+1)$ is $6x^7+12x^6+3x^5$

Step-by-step explanation:

Given: Polynomial $3x^5(2 x^2+4x+1)$

We have to find the product of the given polynomial $3x^5(2 x^2+4x+1)$

Consider the given polynomial $3x^5(2 x^2+4x+1)$

Apply distributive rule, $a(b+c)=ab+ac$

Multiply $3x^5$ with each term in brackets, we have,

$=3x^5\cdot \:2x^2+3x^5\cdot \:4x+3x^5\cdot \:1$

$=3\cdot \:2x^5x^2+3\cdot \:4x^5x+3\cdot \:1\cdot \:x^5$

Apply exponent rule, $a^b\cdot \:a^c=a^{b+c}$

Simplify, we have,

$=6x^7+12x^6+3x^5$

Thus, The product of the given polynomial $3x^5(2 x^2+4x+1)$ is $6x^7+12x^6+3x^5$

almond37 [142]3 years ago

5 0

<span><span>the answer is C.) 6x^7...
</span></span>

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Estimate the circumference of the circle with the given radius or diameter. Use 3.14 for ?. Round to the nearest unit. (Half. 24

Mice21 [21]

Answer:

The perimeter of a circle can be found by using the followinfg expression

P = 2*π*r

where

π = 3.14

r = radius of the circle = half the diameter of the circle

In this case, if we are given the radius, we use

P = 2*π*r

If we are given the diameter, we use

P = 2*π*(D/2) = π*D

1) 27in

radius = 27in

P = 2*(3.14)*(27 in) = 169.56 in

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radius = 79 in

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3 years ago

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What is the square root of 864

skelet666 [1.2K]

There are two ways to evaluate the square root of 864: using a calculator, and simplifying the root.

The first method is simplifying the root. While this doesn't give you an exact value, it reduces the number inside the root.

Find the prime factorization of 864:

$\sqrt{864} = \sqrt{2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 3}$

Take any number that is repeated twice in the square root, and move it outside of the root:

$\sqrt{864} = \sqrt{(2 \cdot 2) \cdot (2 \cdot 2) \cdot 2 \cdot (3 \cdot 3) \cdot 3}$

$\sqrt{2 \cdot 2} = \sqrt{4} = 2$

$\sqrt{3 \cdot 3} = \sqrt{9} = 3$

$\sqrt{(2 \cdot 2) \cdot (2 \cdot 2) \cdot 2 \cdot (3 \cdot 3) \cdot 3} = \sqrt{(4) \cdot (4) \cdot 2 \cdot (9) \cdot 3}$

$\sqrt{(4) \cdot (4) \cdot 2 \cdot (9) \cdot 3} = (2 \cdot 2 \cdot 3) \sqrt{2 \cdot 3} = \boxed{12 \sqrt{6}}$

The simplified form of √864 will be 12√6.

The second method is evaluating the root. Using a calculator, we can find the exact value of √864.

Plugged into a calculator and rounded to the nearest hundredths value, √864 is equal to 29.39. Because square roots can be negative or positive when evaluated, this means that √864 is equal to ±29.39.

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