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3 years ago

Use the remainder theorem to determine whether x=-4 is a solution of x^6+5x^5+5^4+5^3+2x^2-10x-8.

Mathematics

1 answer:

kykrilka [37]3 years ago

4 0

Hello haohaoxNienie!

$\huge \boxed{\mathbb{QUESTION} \downarrow}$

Use the remainder theorem to determine whether x = - 4 is a solution of x⁶ + 5x⁵ + 5x⁴ + 5x³ + 2x² - 10x - 8.

$\large \boxed{\mathbb{ANSWER\: WITH\: EXPLANATION} \downarrow}$

Refer to the attached picture.

<h3>Steps :-</h3>

First find the divisor using the given information (x = - 4).
Now, divide x⁶ + 5x⁵ + 5x⁴ + 5x³ + 2x² - 10x - 8 by x + 4.
We'll get the remainder as 0.
Using the remainder theorem & solving it, we'll get LHS & RHS as 0.
Hence proved.

Answer :- Yes, x = - 4 is a solution of x⁶ + 5x⁵ + 5x⁴ + 5x³ + 2x² - 10x - 8.

__________________

Hope it'll help you!

ℓu¢αzz ッ

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Answer:

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Step-by-step explanation:

Given as :

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The Time taken by car to cover distance = 3 $\frac{1}{2}$ min = $\frac{7}{2}$ min

The speed o car in miles per minute = S miles/min

So, Speed = $\dfrac{\textrm Distance}{\textrm Time}$

Or, S = $\frac{\frac{7}{3}}{\frac{7}{2}}$ mie per min

∴ S = $\frac{2}{3}$ miles per minute

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Or, x = $\frac{\frac{7}{3}}{\frac{7}{120}}$ miles per hours

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Which of the binomials below is a factor of this trinomial?

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In ΔABC, m∠A = 90° and AN is an altitude. If AB = 20 in and AC = 15 in, find BC, BN, NC, AN.

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Since ΔABC is a right triangle, we can use the Pythagorean theorem to find the missing side, BC as shown below.

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Now, since AN is an altitude formed along BC, we can form two smaller triangles that are both similar with ΔABC.
(An image is attached along the file to show the illustrations of the triangles with the larger one.)

Thus, we have ΔNBA~ΔABC and ΔNAC~ΔABC. So, for ΔNBA and ΔABC, we have

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and applying the same process with AN, we have

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We can also use the same method to find the missing sides in ΔANC. But, we can immediately find the value of NC as shown.

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Since ΔANC is a right triangle and two given lengths, we can find the third side, AN, through Pythagorean theorem.

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Use the remainder theorem to determine whether x=-4 is a solution of x^6+5x^5+5^4+5^3+2x^2-10x-8.​​

Use the remainder theorem to determine whether x=-4 is a solution of x^6+5x^5+5^4+5^3+2x^2-10x-8.