1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Natali5045456 [20]
3 years ago
15

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

h. please use synthetic division

Mathematics
1 answer:
telo118 [61]3 years ago
4 0

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

  <u>| 0  -1  -9  -26   -24</u>

   <u> 1    9  26  24    0</u>

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

   <u>| 0  -2  -14   -24</u>

   <u>  1    7    12     0</u>

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

   <u>| 0 -3  -12</u>

    <u> 1    4    0</u>

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.

You might be interested in
Is 110,571 divisible by 3?
MAXImum [283]

Answer:

yes, it is.

Step-by-step explanation:

110,571 divided by 3 is 36857. So, since the answer is not a decimal or a fraction, 110,571 is divisable by 3

3 0
2 years ago
Someone please tell me and maybe ill pay you
rjkz [21]
4x = 6x -10
2x = 10
  x = 5

answer
x = 5
6 0
3 years ago
Help me ASAP I need to turn this assignment right now
STALIN [3.7K]

Answer:268.08

Step-by-step explanation:

7 0
3 years ago
X+3 <br> ——=8 what’s the value for <br> 2. X
irina1246 [14]
I think x equals 13 because 13+3=16 and 16 divided by 2 equals 8
7 0
3 years ago
The top of a ladder rest at a height of 15 feet against the side of a house. If the base of a ladder is 6 ft from the house what
MariettaO [177]

Answer:

16 feet

Step-by-step explanation:

We use Pythagorean Theorem to find the height.

leg of triangle=  height of ladder = 15 feet

The hypotenuse of the formed triangle  = length of ladder = L

base = 6 feet

What is length of ladder?

L^2 = 15^2 + 6^2 = 225 + 36 = 261

L = root(261)  = 16.155 feet

6 0
3 years ago
Other questions:
  • Drawing a jack from a deck of cards, not replacing it, and then drawing another jack or examples of dependent variables.
    14·2 answers
  • Your bill at a register is $153.60. Which would be better for you: A 15% off coupon or a $20 off coupon?
    14·2 answers
  • One of two supplementary angles is five times the other. Find the angles. (Recall that supplementary angles are angles whose sum
    5·1 answer
  • julie started with 20 pieces of gum and gave away x pieces. Karen started with 35 pieces of gum and gave away twice as many as j
    13·1 answer
  • A regular polygon inscribed in a circle can be used to derive the formula for the area of a circle. The polygon area can be expr
    8·2 answers
  • Solve the quadratic equation by graphing: (2 – 7) + 2 = 38 CHOOSE ALL THAT APPLY
    5·1 answer
  • Even numbers between 21 and 43​
    11·2 answers
  • PLEASEEE HELPPP!!!<br> what is the reason for congruence
    9·1 answer
  • write an equation of the line perpendicular to the given line that contains P in point slope form? P (4,8) y=4x-7
    13·2 answers
  • <img src="https://tex.z-dn.net/?f=%5Csqrt%3F%20191" id="TexFormula1" title="\sqrt? 191" alt="\sqrt? 191" align="absmiddle" class
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!