The factors of polynomial expression x^4 + x^2 − 20 is [tex](x - \sqrt{5})(x + \sqrt{5})(x - i \sqrt{5})(x + i \sqrt{5})$[/tex].
We are given that;
The polynomial expression =[tex]x^4 + x^2 − 20.[/tex]
Now,
To factor a polynomial expression, we need to find the common factors of each term and then use the distributive property to write the expression as a product of two or more factors.
For example,[tex]x^4 + x^2 − 20[/tex] can be written as:
[tex]$x^4 + x^2 - 20 = x^2(x^2 + 1) - 20$[/tex]
We can use the difference of squares formula to factor x^2 + 1 and 20:
[tex]$x^2 + 1 = (x + i)(x - i)20 = (2 \sqrt{5})(2 \sqrt{5})[/tex]
where i is the imaginary unit such that i^2 = -1. Now, we can write the expression as:
[tex]$x^4 + x^2 - 20 = x^2(x + i)(x - i) - (2 \sqrt{5})(2 \sqrt{5})$[/tex]
We can use the difference of squares formula again to factor the whole expression:
[tex]$x^4 + x^2 - 20 = (x^2 - 2 \sqrt{5})(x^2 + 2 \sqrt{5})$[/tex]
we can still factor each factor further into prime factors. We have:
[tex]x^2 - 2 \sqrt{5} = (x - \sqrt{5})(x + \sqrt{5})$\\$x^2 + 2 \sqrt{5} = (x - i \sqrt{5})(x + i \sqrt{5})[/tex]
Therefore, by factorization answer will be [tex](x - \sqrt{5})(x + \sqrt{5})(x - i \sqrt{5})(x + i \sqrt{5})$[/tex]
Learn more about factorization here:
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Question 5 (1 point)
Calculate the area of this composite shape. Use the ti key on the calculator. Round answer
to tenths.
10 yd
12 yd
13 yd
13 yd
Area =
yd2
Find X.
Round to the nearest tenth.
Z
20 ft
22ft
X
18 ft
Y
X= [?]°
Answer:
X≈ 70.5°
Step-by-step explanation:
Using the cosine rule in Δ XYZ
cos X = [tex]\frac{y^2+z^2-x^2}{2yz}[/tex]
with x = 22, y = 20, z = 18 , then
cos X = [tex]\frac{202+18^2-22^2}{2(20)(18)}[/tex]
= [tex]\frac{400+324-484}{720}[/tex]
= [tex]\frac{240}{720}[/tex] , then
∠ X = [tex]cos^{-1}[/tex] ([tex]\frac{240}{720}[/tex] ) ≈ 70.5° ( to the nearest tenth )
PLZ HELP PLZ PLZ ILL MARK AS BRAINLIESTT!!!
Answer:
25
Step-by-step explanation:
12345678910112131415161718192021212223242526272829303132333435363738394041424344454647484950
Answer: what what! Confused
Step-by-step explanation:
Answer:
yes
Step-by-step explanation:
A 7-foot roll of aluminum foil costs $1.68. What is the price per inch?
Answer:
Step-by-step explanation:
141.12
kim rented skates for h hours.The rental free was $2.50 per hour. she paid a total a 2.5h=20 b 1.5h=10 c 1.5h=20 d 2.5h=10l of $20
Answer:
2.5h=20
Step-by-step explanation:
:D
how many 2 digit numbers are multiples of five
Answer:
18
Step-by-step explanation:
Hope it helps plz give brainlies! ;D
Will give brainlist!!!!!!
What would be the best method to use in order to solve the following quadratic equation?
X^2 - 3x = 10
Answer:
Use the x method
Step-by-step explanation:
Move the 10 over to the other side and get x^2 - 3x -10 = 0 and solve by finding two numbers that add up to negative 3 but multiply to -10 which would be -5 and 2 so the binomials are (x-5)(x+2)
Answer:
x^2 - 3x = 10
Step-by-step explanation:
Move all terms to the left side.
Use the sum product pattern.
Factor (x-5)(x+2) = 0
Create two separate equations,
x - 5 = 0, and x + 2 = 0
Rearrange and isolate the variable.
x = 5
x = -2
please help with a math problem must show work.
Make the expression below a perfect square by adding in a constant value: x^2+14x+_
Which graph represents the solution of x2 + 9y2 <81 and y2 + 2
Answer:
C on edge
Step-by-step explanation:
the guy above is correct
The graph that represents the given inequalities is required.
The required graph is attached.
The inequalities are
[tex]x^2+9y^2<81[/tex]
[tex]y^2+2<x[/tex]
Converting to general forms
Ellipse
[tex]\dfrac{x^2}{9^2}+\dfrac{9y^2}{9^2}<1\\\Rightarrow \dfrac{x^2}{9^2}+\dfrac{y^2}{3^2}<1[/tex]
So,
[tex]a=\pm9[/tex]
[tex]b=\pm3[/tex]
The vertices of the major axes are [tex](9,0)[/tex] and [tex](-9,0)[/tex]
The vertices of minor axes are [tex](0,3)[/tex] and [tex](0,-3)[/tex]
The center lies on the origin.
Since, the sign of the inequality is [tex]<[/tex] the shaded region will be inside the ellipse excluding the ellipse.
Parabola
[tex]x>1(y-0)^2+2[/tex]
So,
Vertex of parabola = [tex](2,0)[/tex]
Since, the square term is [tex]y^2[/tex] the axis of symmetry is the [tex]x[/tex] axis.
The parabola will open towards the positive x axis.
The shaded region is the area in the parabola excluding the parabola due to the [tex]>[/tex] sign.
Learn more:
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Find each angle or arc measure
Answer:
17
Step-by-step explanation:
34/2 because the measure of the arc is half of what it would normally be because it touched the other side
Carl's class is collecting canned food for a food drive. If the class collects 3 2/3 pounds on the first day and 4 1/4 pounds on the second day, how many pounds of food have they collected so far?
Answer:
7 11/12
Step-by-step explanation:
3 2/3 + 4 1/4 = 3 8/12 + 4 3/12 = 7 11/12
Plz help me with this math problem
Answer:
c and a because x = a smaller number
what does standard devitation mean?
Answer:
a quantity calculated to indicate the extent of deviation for a group as a whole.
Step-by-step explanation:
t1ts
someone, please help !! these are direct and inverse variations, algebra 2. i need them asap !
Answer:
3, 20, 2, and 2.5
Step-by-step explanation:
For each question, they gave you an x and y value. If you substitute them into the equation and then solve for k, you get your answer.
On the first one, x is 12 and y is 1/4. If you put those into the equation they gave you y = k/x, you get 1/4 = k/12
3/12 is 1/4 so the first k is 3.
Second one y = k/x. x is 4 and is 5. So 5 = k/4
20/4 is 5, so the second k is 20.
JUST ANSWER MORE POINTS THAN NEEDED
Answer: b
Step-by-step explanation:
Answer:
The answer would be option B: x < 95
Step-by-step explanation:
The diagram beloon shows a cup in the shape of a right circular conse and yone of its measurements,
cm
10 cm
Which of the following is closest to the volume, in cubic centimeters, of the cup?
Answer:
option c
volume of right circular cone=1/3 *(pi)* r*r *h
Find x in the image above. (I circled x)
Answer:
x = 3.96
Step-by-step explanation:
The ratio for the big triangle is 5:6, so is likely the ratio for the smaller one.
3.3 x 6/5 = 3.96
6 / 3.96 = 1.51515151515
5 / 3.3 = 1.51515151515
Triangles are congruent.
Answer:
3.96 ft.
Step-by-step explanation:
how many solutions does the nonlinear system of equations graphed below have?
Answer:
A. Zero
Step-by-step explanation:
The upside down parabolic graph has no roots because it not linear
How would the numbers -10, 0, and 10 appear on a horizontal number line?
Answer:
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
Step-by-step explanation:
pls help me
Find the surface area of the object.
Answer:
3x3x2=18
3x3x2=18
3x3x2=18
1x3x9=27
18+18+18+28=81 81 cm
Step-by-step explanation:
Someone help me with this pls
Answer:
=8^-8 × 8^3
= 8^-8+3
=8^ -5
What is the percent of increase from 4,000 to 10,000?
Answer:
150%
Step-by-step explanation:
Percent change = [tex]\frac{New - Old}{|Old|}[/tex] × 100%
=> [tex]\frac{10000-4000}{4000}[/tex] × 100
=> [tex]\frac{6000}{4000}[/tex] × 100 = 150% (increase)
Point P is located at (6, -4), while point Q is located at (6, 4). How are the two points related?
HELP ME PLZZZZZZZZ!!!!!
Answer:
They have the same x value.
Step-by-step explanation:
Explain how you could find the area of the figure below?? Hellppp
Answer:
How you would find area of any shape is you would multiply length x width x height.
Step-by-step explanation:
What do A and B equal?
PLEASE ANSWER I WILL GIVE A BRAINLIEST
Answer:
a=2
b=2
Step-by-step explanation:
This is a special 45-degree right triangle. Two angles equal 45 degrees, and then there is a right triangle. In these triangles, the hypotenuse is equal to [tex]k*\sqrt{2}[/tex] where k is equal to the legs (a and b). So, to find the legs divide [tex]k*\sqrt{2}[/tex] by [tex]\sqrt{2}[/tex]. This equals 2, and since a and b are congruent both a and b equal 2.
The students of a school fill 5 buses for a field trip. Each class fills bus. How many classes are riding on the buses?
Answer:
The answer is 5
Step-by-step explanation:
Because each bus is assigned 1 class and there is only five buses so there are 5 classes
What is the area of a rectangle with side
lengths x - 4 and 5x + 7?
I need help quick. ASAP.