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3 years ago

Use the remainder therom to find the remainder when x^4-3x^2-9x+4 is divided by x-3

1 answer:

8 0

If we can write the given polynomial as

$\underbrace{p(x)}_{\text{given}}=q(x)(x-3)+r(x)$

that is, write $p(x)$ as the product of two factors plus some remainder term, then we can simply plug in $x=3$ to determine the remainder term because that would force the $q(x)$ term to vanish.

$p(x)=x^4-3x^2-9x+4\implies p(3)=31$

so the remainder upon dividing $p(x)$ by $x-3$ is 31.

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Given the polynomial 21x^4+3y-6x^2+34 1. What polynomial must be subtracted from it to obtain 29x^2-7? 2. What polynomial must b

zysi [14]

Answer:

$21x^4+3y-35x^2+41$ must be subtracted

As you can see, we added -x+2 to this polynomial to obtain a first degree polynomial. (Though really anything with an x would do. For example, 3x, 2221x, or -224x would all work)

Step-by-step explanation:

We have the following polynomial

$21x^4+3y-6x^2+34$

And need to find a polynomial to subtract from it to get

$29x^2-7$

This means that if we subtract these two polynomials, we will get our desired polynomial

$21x^4+3y-6x^2+34-(29x^2-7)\\\\21x^4+3y-6x^2+34-29x^2+7\\\\21x^4+3y-35x^2+41$

Just to be sure, we can then check our work by finding the difference of the first polynomial and the one that we just found

$21x^4+3y-6x^2+34-(21x^4+3y-35x^2+41)\\\\21x^4+3y-6x^2+34-21x^4-3y+35x^2-41\\\\-6x^2+34+35x^2-41\\\\29x^2-7$

As we got the desired result, we know that this answer is correct.

And now for the second part of the problem. What polynomial must be added to it to obtain a first degree polynomial?

Recall that a first degree polynomial is one that has the total sum of 1. For example the polynomial x+5 is a first degree polynomial, but x+y+5 has a degree of 2.

This means that our desired polynomial needs to only have some amount of x's and constants.

We can do the same thing as the first time and simply subtract our desired result from the first polynomial. For simplicity, let us use the simple polynomial x+2

$21x^4+3y-6x^2+34-(x-2)\\\\21x^4+3y-6x^2+34-x+2\\\\21x^4+3y-6x^2-x+36$

As you can see, we added -x+2 to this polynomial to obtain a first degree polynomial. (Though really anything with an x would do. For example, 3x, 2221x, or -224x would all work)

7 0

3 years ago

Twenty boys signed up for the school play. The number of girls who signed up was 195% of the number of boys. At the auditions, o

Firlakuza [10]

20 boys signed up
# of girls who signed up was 195% of the number of boys who signed up

Find 195% of 20:

1.95 * 20 = 39

So 39 girls signed up.

To find out what percent of girls who signed up for the play attended the auditions, divide 26 to the total number of girls who signed up:

26 / 39 = 0.666666667

Multiply by 100:

0.666666667 * 100 = 66.6666667%

So approximately 66.67% or 66 2/3%

7 0

3 years ago

Please If you plan to help me with any of these and respond to I would be grateful please show that this application is for good

valentina_108 [34]

Answer:

Step-by-step explanation:

Whether you’re job searching, working on your professional development, or building your career, you’ve probably been in a situation that warranted showing appreciation and gratitude. Perhaps you received a job lead and a pep talk from a former colleague. Maybe you had an informational interview with someone who has now taken you under their wing and is serving as a mentor. It might even be a family member who’s your greatest fan. Whatever the situation, one way to show gratitude is to write a thank-you note that expresses your appreciation.

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3 years ago

sheila works for a fishing companyshe is paid $20 per day and an additional $2 fo ea lobster she catches. she wats to know how m

kari74 [83]

5 days x $20 payment each day=$100
Goal Profits=$130
$130-$100=$30
$30/$2 per lobster= 15 lobsters

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3 years ago

Brainliest!!!!! Please Help

Maru [420]

The wiggly line is a function and the circle thingy is relation since it does not pass the line test

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4 years ago