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3 years ago

15

Determine whether the function h left parenthesis x right parenthesis equals 6 x cubed minus one half x plus 8 is a polynomial f

unction. If it is a polynomial function, then state the degree and leading coefficient.

1 answer:

kupik [55]3 years ago

5 0

$h(x) = (6x)^{3} - 1.5 x + 8 = 216 {x}^{3} - 1.5x + 8$

h is polynomial and its degree is 3 and the leading coefficient is equal to 216

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6. Consider the polynomial p(x) = x^2 + kr^2 +x+6. Find a value of k so that x+1 is a factor of P. Find all the zeros of P.

Nikitich [7]

If <em>x</em> + 1 is a factor of <em>p(x)</em> = <em>x</em>³ + <em>k</em> <em>x</em>² + <em>x</em> + 6, then by the remainder theorem, we have

<em>p</em> (-1) = (-1)³ + <em>k</em> (-1)² + (-1) + 6 = 0 → <em>k</em> = -4

So we have

<em>p(x)</em> = <em>x</em>³ - 4<em>x</em>² + <em>x</em> + 6

Dividing <em>p(x)</em> by <em>x</em> + 1 (using whatever method you prefer) gives

<em>p(x)</em> / (<em>x</em> + 1) = <em>x</em>² - 5<em>x</em> + 6

Synthetic division, for instance, might go like this:

-1 | 1 -4 1 6

... | -1 5 -6

----------------------------

... | 1 -5 6 0

Next, we have

<em>x</em>² - 5<em>x</em> + 6 = (<em>x</em> - 3) (<em>x</em> - 2)

so that, in addition to <em>x</em> = -1, the other two zeros of <em>p(x)</em> are <em>x</em> = 3 and <em>x</em> = 2

6 0

3 years ago

Six friends share 4 apples equally. How much

zvonat [6]

4 divided by 6 is 0.6666666667

3 0

3 years ago

List the single-digit divisors of 2100.<br> I really need help

liberstina [14]

Answer:

1, 2, 3, 4, 5, 6, 7

Step-by-step explanation:

<u>Prime factors of 2100 are:</u>

2100 = 2*2*3*5*5*7

<u>The single-digit divisors are:</u>

1, 2, 3, 2*2= 4, 5, 2*3= 6, 7

-----------------------------------------------------------------

<u>Another solution is you divide 2100 by all numbers 1 through 9 and list those divisible:</u>

2100/1 = 2100, yes
2100/2 = 1050, yes
2100/3 = 700, yes
2100/4 = 525, yes
2100/5 = 420, yes
2100/6 = 350, yes
2100/7 = 300, yes
2100/8 = 262.5, no
2100/9 = 233.33, no

So all the numbers from 1 to 7

5 0

3 years ago

A local citizen wants to fence a rectangular community gardenn. The length of the garden should be at least 110ft,and the distan

Arte-miy333 [17]

The question is incorrect
the correct question is
A local citizen wants to fence a rectangular community garden. The length of the garden should be at least 110 ft,and the distance around should be no more than 380 ft. Write a system of inequality that model the possible dimensions of he garden. Graph the system to show all possible solutions

let
x---------------> t<span>he length of the garden
</span>y---------------> the wide of the garden

we know that
x>=110
2x+2y <=380---------------> x+y <= 190

Part A) <span>Write a system of inequality that model the possible dimensions of he garden
</span>
the answer part A) is
x>=110
x+y <= 190

Part B) <span>Graph the system to show all possible solutions

using a graph tool
see the attached figure
the solution is the triangle show in the figure

</span><span>the possible solutions of y (wide) would be between 0 and 80 ft
</span>the possible solutions of x (length) would be between 110 ft and 190 ft

5 0

3 years ago

Round to the given place value hundreds and tens 547 , 609 and 990

myrzilka [38]

The first number will be 500
the second number will be 600
and the last number will be 990

8 0

4 years ago

Read 2 more answers