Determine the leading coefficient of the polynomial p, which has exactly three roots: -1, 1 and 2, and for which p(3) = 24 is true.


Answers

Answer 1

Answer:

The polynomial is [tex]x^3-2x^2-x+2[/tex]

Leading coefficient is 1

Step-by-step explanation:

We need to determine the leading coefficient of polynomial p having roots

-1,1 and 2 and p(3)=24

Roots of polynomial are: -1,1,2

We can write them as:

x=-1, x=1, x=2

x+1=0, x-1=0, x-2=0

or:

(x+1)(x-1)(x-2)=0

Multiplying the terms to find the polynomial:

[tex](x+1)(x-1)(x-2)=0\\(x(x-1)+1(x-1))(x-2)=0\\(x^2-x+x-1)(x-2)=0\\(x^2-1)(x-2)=0\\x^2(x-2)-1(x-2)=0\\x^3-2x^2-x+2=0[/tex]

So, The polynomial is [tex]x^3-2x^2-x+2[/tex]

The leading coefficient is the coefficient with highest power So, in polynomial we have highest power [tex]x^3[/tex] so, leading coefficient is 1


Related Questions

The ratio of red marbles to black marbles is 4:7. If the bag consists of 77 marbles in all, how many red marbles are in the bag?

Answers

Answer:

28:49

Step-by-step explanation:

4:7 is equal to 11 total marbles and if there are 77 you would multiply each number by 7

5. Select ALL of the following expressions that are linear functions (they do not need to be in slope-intercept form).
y2 = 5x +2
2x + 4 = 3x - 8
y = 3x - 2
y + x2 = 12
y = x2 + 2x
1
3x + -y = 24

Answers

Answer:

The following are the LINEAR functions.

[tex]2x\:+\:4\:=\:3x\:-\:8[/tex][tex]y = 3x - 2[/tex][tex]1[/tex][tex]3x\:+\:-y\:=\:24[/tex]

Step-by-step explanation:

We know that linear functions are the equations with a straight line graph in an XY plane.

Also, a linear function is a function of the form

[tex]f(x)=mx+b[/tex]

where m is the slope and b is the y-intercept. The only power of the variable is 1.

So, from the given expressions we can determine that:

1) [tex]y^2=\:5x\:+2[/tex]

[tex]y^2=\:5x\:+2[/tex]  is NOT a linear function because the power of y is 2, hence the graph won't be a straight line. Therefore, it is not a linear function

2) [tex]2x\:+\:4\:=\:3x\:-\:8[/tex]

[tex]2x\:+\:4\:=\:3x\:-\:8[/tex]

[tex]x=12[/tex]

This is a linear equation is an equation of a straight line, written in one variable.  The only power of the variable is 1

3) [tex]y = 3x - 2[/tex]

[tex]y = 3x - 2[/tex] is a linear function because it is of the form [tex]f(x)=mx+b[/tex] and the power of its x and y variables is 1. Hence, the function has a straight line graph.

4) [tex]y\:+\:x^2\:=\:12[/tex]

[tex]y\:+\:x^2\:=\:12[/tex] is NOT a linear function because the power of x is 2, hence the graph won't be a straight line. Therefore, it is not a linear function.

5) [tex]y\:=\:x^2\:+\:2x[/tex]

[tex]y\:=\:x^2\:+\:2x[/tex] is NOT a linear function because the power of x is 2, hence the graph won't be a straight line. Therefore, it is not a linear function.

6) [tex]1[/tex]

[tex]1[/tex] is a constant function and a constant function is also considered linear in this context, as it is a polynomial of degree [tex]0[/tex] or is the [tex]0[/tex] polynomial.

7) [tex]3x\:+\:-y\:=\:24[/tex]

[tex]3x\:+\:-y\:=\:24[/tex] is a linear function as the power of its x and y variables is 1. Hence, the function has a straight line graph. Therefore, it is a linear function.

In a  summary, the following are the LINEAR functions.

[tex]2x\:+\:4\:=\:3x\:-\:8[/tex][tex]y = 3x - 2[/tex][tex]1[/tex][tex]3x\:+\:-y\:=\:24[/tex]

What set of numbers is arranged from largest to smallest? (Mind the blue on one of the answers)

Answers

Answer:

B

Step-by-step explanation:

it orders the negative things in the top right correctly because the bigger the negative number in the top right the lower the number is aka the greater of a negative number there is

The answer I got was B
Hope this helps:)

Which equation would intersect the line on the graph at the point (-2,
-2)?

Answers

Answer:

Y = 0x-2.

Step-by-step explanation:

I don't want the question of my teachers being in my b or I am a good time wi and I am

(37-4x²+ 3y) x= 2 and y=3​

Answers

Correct answer is 30

hii guys happy chota dipawali​

Answers

Answer:

yay thats so coolllllllll

Hiiiiiii :) how are you all?

1/2(x+2)=5(x+2) solve the following completely

Answers

Answer:

X is equalled to '' - 2''

Step-by-step explanation:

If you need an explanation, leave a comment ;) As my hand writing is very messy. I'll write it here if you want.

Cheers! :)

What is the volume of the following rectangular prism?

Answers

Answer:

1/2 * 7/4 = 7/8

Thank you and please rate me as brainliest as it will help me to level up

Write the following fractions in order of size
1/3
3/4
1/4
7/12
1/2
Start with the smallest fraction.​

Answers

Ans wer 7/12 3/4 1/3 1/2

Step-by-step explanation:

Evaluate the expression for f = 20.
122 - 2f
9. Show your work:
A. 82
B. 100
C. 140
D. 2400

SHOW YOUR WORK PLZSSSSSSS

Answers

Answer:

82

Step-by-step explanation:

2(20)=40.

122-40=82.

Find the geometric mean of the data below:

2, 5, 7

Answers

Answer:

[tex]\sqrt{70}[/tex]

Step-by-step explanation:

Given data:

         2, 5 , 7

The geometric mean is a measure of central tendency of a data set which utilizes the product of their values

To find the geometric mean of the given values;

multiply them togetherfind the square root;

Geometric mean  = [tex]\sqrt{2 x 5 x 7 }[/tex]  

Geometric mean  = [tex]\sqrt{70}[/tex]

Which one is the linear function of x.
I know it is not A or C

Answers

Answer: d

Step-by-step explanation:

Explain the Error

Find the error in the solution, and then solve it correctly.

7x + 21 + 6x = 4

7x + 21 = -2

7x = -23

-23

7

(select) was subtracted from the left side, but (select) was subtracted from the right side. The

Subtraction Property of Equality states that you can subtract the same number from each side and the

equation will remain true. But 6x and 6 are not the same number (unless x is (select)).

X =

Answers

Answer:

Step-by-step explanation:

7x+21+6x=4 combine terms

13x+21=4  subtract 21 from both sides

13x= -17 divide by 13

x= -17/13

Write an equation of the line that passes through the given point and is parallel to
the given line.
10. (14, 3); 2y - x - 8

Answers

Answer:

y = x - 23

Step-by-step explanation:

When
4a- a x 3a + 7a
is simplified it is equivalent to?​

Answers

Answer:

-3a^2+11a

Step-by-step explanation:

Answer:

4a-a×3a+7a

or, 3a×3a+ 7a

or,9a+7a

or,16a

:. a =16

What is the value of a in the equation a = 2 + 3a + 8? (5 points)

Group of answer choices

5

10

−5

−10

Answers

Step-by-step explanation:

a = 2 + 3a + 8

a = 10 + 3a

a - 3a = 10

-2a = 10

a = -5

help im being timed what is the area of the rectangle?!

Answers

Answer:

30

Step-by-step explanation:

Hope this helps.

25 POINTS!! which point is a solution to the inequality shown in this graph 3,-1 -3,-3

Answers

Answer:

(3, 3)

Step-by-step explanation:

Answer:

Step-by-step explanation:

i think its (3,-1)

I NEEDA KNOW IF IM RIGHT , IDK HELP

Answers

Answer:

CD and DE are perpendicular because their slopes are -1/3 and 3

Step-by-step explanation:

Perpendicular lines will always have the opposite reciprocal.

...... help lots of points available (plz answer it)

Answers

The correct option is answer C :)

what multiples to give you -30 and adds to give you -13

Answers

Answer:

This is impossible

Step-by-step explanation:

But try -10x-3=30 -10+-3=-13

Please help me ASAP!

Answers

Answer:

angle 4

Step-by-step explanation:

(Will mark brainliest and give $5 Starbucks digital card Include SC!!!) For which set of triangles can you immediately use the AAS congruence criteria to prove them congruent?(1 point)
1. triangles STU and VWX, where ∠T≅∠W, ∠U≅∠X, and SU≅VX

2. triangles GHI and JKL, where ∠G≅∠J, ∠H≅∠K, and GH≅JK

3. triangles MNO and PQR, where ∠N≅∠Q, MN≅PQ, and NO≅QR

Answers

I'm not so sure about this answer, but i remember doing something similar to this. I think it's 3.

Q» 7. A party hat is shaped like a cone. The dimensions of the party hat are shown in the diagram On O 1,017.88 in. O 254.47 in.3 O 84.82 in. 9 in. O 339.29 in. 3 CLEAR ALL 6 in. Which measurement is closest to the volume of the party hat in cubic 2.​

Answers

Answer:

The answer is 84.82 in^3

Step-by-step explanation:

what is the value of this equation below when y=8 and z=8
9y+3z

Answers

Answer:

96

Step-by-step explanation:

Step-by-step explanation:

=9y+3z

=9×8+3×8

=72+24

=96

hope it help u.

GEOMETRY QUESTION, HELP PLEASEEE.

Answers

Answer:

The pre-image C is (2, 5)

Step-by-step explanation:

If the point (x, y) rotated about the origin by angle 90° clockwise, then its image is (y, -x)If the point (x, y) rotated about the origin by angle 180° clockwise, then its image is (-x, -y)If the point (x, y) rotated about the origin by angle 270° clockwise, then its image is (-y, x)

∵ Point C was rotated 270° clockwise around the origin

C' = (-5, 2)

→ By using the 3rd rule above

∵ The image of the point (x, y) is (-y, x)

∴ (-y, x) = (-5, 2)

→ That means -y = -5 and x = 2

x = 2

∴ -y = -5

→ Divide both sides by -1

y = 5

The pre-image C = (2, 5)

Answer correctly please !!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!!!!!!!

Answers

3x - 20 + 3x + 5 = 111

Combine like terms
6x - 15 = 111

Add 15 to each side.

Evaluate
6x = 126
x = 21

Plug x back into the equation for angle EFG.
EFG = 3x -20
3(21) - 20
EFG = 43 degrees

Answer:

[tex] m\angle EFG =43\degree[/tex]

Step-by-step explanation:

[tex] m\angle EFG +m\angle GFH = m\angle EFH\\\\

(3x-20)\degree + (3x+5)\degree =111\degree \\\\

(3x-20+3x +5)\degree =111\degree \\\\

(6x-15)\degree =111\degree \\\\

(6x-15) =111 \\\\

6x = 111 + 15\\\\

6x = 126\\\\

x = \frac{126}{6}\\\\

x = 21\\\\

m\angle EFG = (3x-20)\degree\\\\

m\angle EFG = (3\times 21-20)\degree\\\\

m\angle EFG = (63-20)\degree\\\\

m\angle EFG =43\degree\\[/tex]

how do i solve -3=-2x+1 by graphing?

Answers

Answer:

x = 2

Step-by-step explanation:

-3 = -2x + 1

minus 1 to the both sides

-3 -1 = -2x

-4 = -2x

divide both sides by -2

x = 2

What’s the answer to this? Thanks!

Answers

Answer:

D

Step-by-step explanation:

I used a triangle calculator I'm not really sure how to calculate it by hand. if the angle of sides 4 and 15 is set to 1 then the min is 11.33 and if the andle of sides 4 and 15 are set to 179 then the max is 18.99952

Sorry if this isnt enough, but i am sure.

Answer:

D.  11 < x < 19.

Step-by-step explanation:

The third side x is between 11 and 19 cm.

Consider sides AB (length 4) and BC (length 15) of the triangle.

Consider the angle between AB and BC is slightly less than 180 degrees.  To get from point A to point C, we have to travel almost the entire length of A to C, which is from A to B and then B to C, so a bit less than 19 cm.

Consider the angle between AB and BC is slightly more than 0 degrees.  To get from point A to point C, we subtract the length of AB (because we're already further along BC), so 15 - 4, a bit greater than 11.

9-2*x=35
A. -13
B. -22
C. 48

Answers

Answer:

x= -13 (a)

Step-by-step explanation:

-2x=35-9

-2x=26

x=-13

hope this helps x.

Answer:

-13

Step-by-step explanation:

9-2/x=35

9-2/x=35

-2/x=35-9

-2/x=26

-2=26x

26x=-2

x=-1/13

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