The difference of two numbers is five. Five times the lesser number minus the greater number is -9. What are the two numbers?

2. Factor f(x) = x4 + 10x3 + 35x2 + 50x + 24 completely showing all work and steps with synthetic division. Then sketch the grap

telo118 [61]

We need to use rational root theorem to find out roots here.

The rational root theorem states that if p(x) is a polynomial with integer coefficients and if $\frac{p}{q}$ is a zero of p(x) then p is a factor of constant term and q is a factor of leasing term coefficient.

Here factors of constant term are 1,2,3,4,6,8,12,24,-1,-2,-3,-4,-6,-8,-12, and -24.

And factors of leading coefficient is -1,1.

Hence possible roots may be -1,1,-2,2,-3,3,-4,4,-6,6,-8,8,-12,12,-24 and 24.

Let us plugin these in f(x) to find zeroes.

$f(-1)=(-1)^{4}+10(-1)^{3}+35(-1)^{2}+50(-1)+24 =1-10+35-50+24=0$

Hence x=-1 is a zero which means x-(-1)=x+1 is a factor.

Let us use synthetic division to find quotient.

-1 | 1 10 35 50 24

| 0 -1 -9 -26 -24

1 9 26 24 0

Hence quotient is $x^{3} +9x^{2} +26x+24$

Since all coefficients are positive, root must be negative. Let's plugin all remaining negative numbers in the quotient.

$(-2)^{3}+9(-2)^{2}+26(-2)+24 = 0$

Hence x+2 is another factor.

Let us find quotient again using synthetic division.

-2 | 1 9 26 24

| 0 -2 -14 -24

1 7 12 0

Hence quotient is $x^{2} +7x+12$

Again we got quotient with all positive coefficients, let us plugin remaining negative numbers from rational root theorem.

$(-3)^{2}+7(-3)+12=-9-21+12=0$

Hence x+3 is also a factor.

Let us find quotient using synthetic division.

-3 | 1 7 12

| 0 -3 -12

1 4 0

Hence quotient is x+4.

So, $f(x)=x^{4}+10x^{3}+35x^{2}+50x+24 =(x+1)(x+2)(x+3)(x+4)$

Please have a look at the graph attached.

4 0

3 years ago

What is 6ft to 4 yards as a fraction in simplest form

Vesna [10]

1yard =3ft so 》 6ft/4×3ft=6/12=1/2

3 0

3 years ago

A company has $6582 to give out in bonuses. An amount is to be given out equally to each of the 32 employees.

expeople1 [14]

A) His estimate is incorrect, since he has increased a figure to the amount that each employee would receive.

B) Rounded to the nearest dollar, each employee would receive $ 209.

Since a company has $ 6582 to give out in bonuses, and an amount is to be given out equally to each of the 32 employees, and A) a manager, Jake reasoned that since 32 goes into 64 twice, each employee will get about $ 2000 , to determine if his estimate is correct, and B) determine how much will each employee receive, rounded to the nearest whole dollar, the following calculations must be performed:

A)

2000 x 32 = 64000
200 x 32 = 6400

Therefore, his estimate is incorrect, since he has increased a figure to the amount that each employee would receive.

B)

6582/32 = X
208.68 = X

Therefore, rounded to the nearest dollar, each employee would receive $ 209.

Learn more about maths in brainly.com/question/8865479

4 0

2 years ago

Solve 33 1/2 of 48 Plz thanks <3

SIZIF [17.4K]

Answer:

1608

Step-by-step explanation:

5 0

2 years ago

The Enterprise High School girl's soccer team won 80% of their games last year if the team won 12 games how many did they play?

jasenka [17]

I gizg A Tduuiy gf dryfchv u

3 0

2 years ago