Find the values of a and b given that the polynomial P(x) = x^3+ ax^2 +x+b, is divisible by
both x-1 and x + 3.​

Answers

Answer 1

Answer:

a=4

b=-6

Step-by-step explanation:

If P(x) is divisible by x-c, then P(c)=0.

So P(1)=0 implies 1^3+a1^2+1+b=0

and

P(-3)=0 implies (-3)^2+a(-3)^2+-3+b=0

So notice we have a system to solve.

Let's simply it.

First equation:

1^3+a1^2+1+b=0

1+a+1+b=0

2+a+b=0

a+b=-2

Second equation:

(-3)^3+a(-3)^2+-3+b=0

-27+9a-3+b=0

9a+b-30=0

9a+b=30

Let's put our system together:

a+b=-2

9a+b=30

This is setup so if we subtract the equations b will eliminate allowing us to solve for a:

-8a=-32

a=4

If a=4 and a+b=-2, then 4+b=-2 giving us b=-6.

a=4

b=-6


Related Questions

How do I solve x squared 3 + 4 when x = 6

Answers

Answer:

Step-by-step explanation:

3 + 4 x = 6

Plot:

Plot

Alternate forms:

4 x = 3

4 x - 3 = 0

Number line:

Number line

Solution:

x = 3/4

please anybody help me to solve this question please help me​

Answers

Step-by-step explanation:

Akmal=A

Aisyah=B

Atikah=C

B=m

A=2m

C=2m+25

C-B=?

2m+25-m=

=m+25

Which system of equations is shown by the graph?

Answers

Answer:

y-x=15 and 25+2x=y

Step-by-step explanation:

What are two numbers that multiply to 18 but add to -9?

Answers

Answer:

-6 and -3

-6 x -3 = 19

-6 + -3 = -9

Answer:

-6 x -3 = 18

-6 + -3= -9

Step-by-step explanation:

hope it helps!!

If f (-8)= 0 and f (x)= x^3-x^2-58x+112, find all the zeros of f(x) write your answer in ascending order

Answers

Answer:

The zeros in ascending order are 2, 7, 8.

Step-by-step explanation:

Since f(-8) = 0, it means that (x + 8) is a factor of the function f(x)= x³ - x² - 58x + 112.

I have attached the long division of this to get the remaining factors of the polynomial function.

The remaining factor is;

x² - 9x + 14

Using quadratic formula via a calculator, we have; x = 7 and x = 2

Thus,the zeros of the polynomial function f(x)= x³ - x² - 58x + 112 in ascending order are;

2, 7, 8

Fred is baking cookies for a school sale. It takes 3/4 cups of sugar to make on batch of cookies how many cups of sugar does he need to make 9 batches

Answers

Answer:

6 3/4 cups.

Step-by-step explanation:

Multiply 3/4 by 9.

Hope this helps!

Liliana bought a book for $13. She is selling the book for $24. What is the percent markup on the price of the book? Round to the nearest hundredths place.​

Answers

Answer: 2.5

Explanation!:

Erik read a total of 4 books over 2 months. After belonging to the book club for 17 months, how many books will Erik have read in all? plss hep me thank you!!

Answers

Answer: 34 books

Step-by-step explanation:

Since Erik read a total of 4 books over 2 months. This means that every month, he read (4/2) = 2 books.

After belonging to the book club for 17 months, the number of books that he'll have read will be the number of books he read per month multiplied by 17 months. This will be:

= 2 × 17

= 34 books

Solve the given system of equations.

4x+5y=10
-x-8=3y

Answers

X= 10

y=-6



Hope this helps

how many solutions does equation 4x + 3 - 1 = 2(2x + 2) - 2x have explain your reasoning.

Answers

Answer:

Anwser: X=1

4x+3-1=2(2x+2)-2x

4x+2=4x+4-2x

4x+2=2x+4

-2 -2x

2x=2

X=1

Step-by-step explanation:

Answer:

one solution

Step-by-step explanation:

Given

4x + 3 - 1 = 2(2x + 2) - 2x ← distribute parenthesis on right side

4x + 2 = 4x + 4 - 2x

4x + 2 = 2x + 4 ( subtract 2x from both sides )

2x + 2 = 4 ( subtract 2 from both sides )

2x = 2 ( divide both sides by 2 )

x = 1

pls help me, i will actually give BRAINLIEST:

What is the transformation shown in the graph?

Answers

Answer:

Step-by-step explanation:

it's rotated by 90° about the origin , in a clock wise direction

James had $43 on his birthday he received $25. Write and solve and equation to find out how much money he has now.

Answers

Answer:

43+25=68

Step-by-step explanation:

Please Help. Im in a hurry!!

Answers

Answer:

A

Step-by-step explanation:

How do angles of depression and elevation relate when solving problems involving right triangles?

Answers

The relationship between the angle of elevation and the angle of depression is called alternate interior angles theorem. As such, these angles are congruent and equal. Hope this helps! Mark brainly please!

Please help me with my geometry work

Answers

-distance/length?
-line
1.Circumference is the perimeter of a circle
2. They both are the measure of the distances around each shape.

What is the slope of Y-9=-2(x-8)

Answers

12.5 is x and 25 is y

what's 60.540 to the nearest degree?

Answers

Answer:

don't know :)

Step-by-step explanation:

The local pizza restaurant offers free delivery if you live within a 6-mile radius of the restaurant. The restaurant is located at the origin. Ada’s house is 4 miles west and 5 miles north of the restaurant at point (–4, 5). Does Ada’s house lie on or within the circle representing the area that gets free delivery?

a. No, the distance from the restaurant to Ada’s house is miles, which is greater than the 6-mile maximum radius.
b. Yes, the distance from the restaurant to Ada’s house is exactly 6 miles.
c. No, the distance from the restaurant to Ada’s house is 7 miles, which is greater than the 6-mile maximum radius.
d. Yes, the distance from the restaurant to Ada’s house is miles, which is less than the needed 6-mile radius.

Answers

Answer:

A.......No, the distance from the restaurant to Ada’s house is  miles, which is greater than the 6-mile maximum radius

Step-by-step explanation:

Using the distance between two points, it is found that the correct option regarding whether Ada’s house lie on or within the circle representing the area that gets free delivery is given by:

a. No, the distance from the restaurant to Ada’s house is [tex]\sqrt{41}[/tex] miles, which is greater than the 6-mile maximum radius.

What is the distance between two points?

Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

In this problem, we want to find the distance between the restaurant at the origin (0,0) and Ada's house at point (-4,5), hence:

[tex]d = \sqrt{(5 - 0)^2 + (-4 - 0)^2} = \sqrt{41} > 6[/tex]

Greater than 6 miles, hence option a is correct.

More can be learned about the distance between two points at https://brainly.com/question/18345417

Which list shows all the possible unique outcomes if Emilio chooses 3 buttons at one time from his jar?

Answers

Need to know how many buttons in the jar and what colours they are

Write an equation in slope-intercept form for the line that passes through the
given point and is parallel to the graph of the given equation.
(4, -6), y=-3/4x+1

Answers

Answer:

[tex]y=-\frac{3}{4}x-3[/tex]

Step-by-step explanation:

The slope will be the same as the one in the given equation since they are parallel, you can substitute the x and y of the given point into the given equation, replacing the 1 with m to get m in the equation.

I hope this helps :)

Judah rides his bike 15 miles in 1/2 an hour.How many miles does he ride in one hour?

Answers

30 miles in one hour
1/2 and hour=30 minutes. 1 hour=60 minutes. 30*2=60. So, 15*2=30 must be the answer.

solve for y
2y-13=11

Answers

Answer:

y = 12

Step-by-step explanation:

2y - 13 = 11

add

2y = 24

divide

y = 12

2y   -   13   =   11

        + 13    + 13

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

2y   =  24

/2        /2

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

y      =  12

What is the slope of this line? Please awnser

Answers

Answer:

-1/2

Step-by-step explanation:

The rise is -1 and the run is 2, the slope is rise over run

I hope this helps :)

The answer should be -1/2

What would it be? thank you

Answers

Answer:

C = 43.98 inches; A = 153.94 square inches

Step-by-step explanation:

2*pi*(7)=43.98

pi*(7)^2=153.94

2. A store sells an assortment of batteries
in bulk packs of 300. Of those batteries.
90 are AAA size. What percent of the
pack are AAA-size batteries?
A 10%
B 30%
C 60
D 90
Answer quick PLZZ no website

Answers

Answer:

30%

Step-by-step explanation:

# of bulk packs = 300

# of triple As  = 90

% = 90 / 300 * 100%

% = .3 * 100%

% = 30%

Answer:

b. 30%

Explanation:

90 ÷ 300 × 100%

= 9 ÷ 30 × 100%

= 0.3 × 100%

= 30%

i hope this helps! :D

which sign do i use??/

Answers

the greater than symbol i presume

Given sin y = -4/5, where π < y < 3π/2, and cos x = 12/13, where 0 < x < π/2. Find the exact value of sin (x - y).

Please show all the exact steps in order I am really lost on how to solve this.

Answers

Answer:

Solution given:

sin y = -4/5

p/h=4/5

p=4

h=5

b=√{5²-4²)=3

cos y = b/h=-3/5

again

cos x=12/13

b/h=12/13

b=12

h=13

p=√(13²-12²)=5

sin x=p/h=5/13

now

sin[x-y]=sinxcosy-cosxsiny

=5/13×-3/5-(12/13×-4/5)=33/65 is your answer.

What is the slope if you are given the following ordered pairs? (Simplify)
(-1,6) & (8,6)

Answers

Answer:

7/2

Step-by-step explanation:

y2-y1/x2-x1

(6-(-1)/8-6) = 7/2

i dont know the answer!

will give brainlist

Answers

Answer:

second answer

Step-by-step explanation:

yards is commonly used for large sparse area measurements

The radius of a circle is 3.8 feet find the diameter

Answers

Answer:

7.6

Step-by-step explanation:

radius is half the diameter so multiply 3.8 times 2.

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