How can I factorise (2x cubed - 5x + 3) ?

Answers

Answer 1

Answer: $2x^3-5x+3=2x^3-2x-3x+3\n\n=2x(x^2-1)-3(x-1)\n\n=2x\underbrace{(x^2-1^2)}_(use\ (*))-3(x-1)\ \ \ |(*)\ a^2-b^2=(a-b)(a+b)\n\n=2x\underbrace{(x-1)}_((**))(x+1)-3\underbrace{(x-1)}_((**))\n\n=(x-1)[2x(x+1)-3]\n\n=(x-1)\underbrace{(2x^2+2x-3)}_((***))\n\n(***)\ 2x^2+2x-3\to a=2;\ b=2;\ c=-3\n\nx=(b^2\pm√(b^2-4ac))/(2a)$

$therefore\nx=(-2\pm√(2^2-4(2)(-3)))/(2(2))=(-2\pm√(4+24))/(4)=(-2\pm√(28))/(4)=(-2\pm√(4\cdot7))/(4)=(-2\pm2\sqrt7)/(4)\n\n=(-1\pm\sqrt7)/(2)\n\nso,\ the\ answer:\n\n(x-1)\cdot2\left(x-(-1-\sqrt7)/(2)\right)\left(x-(-1+\sqrt7)/(2)\right)\n\n=\boxed{(x-1)(2x+1+\sqrt7)\left(x+(1-\sqrt7)/(2)\right)}=\boxed{(1)/(2)(x-1)(2x+1+\sqrt7)(2x+1-\sqrt7)}$

Answer 2

Answer: 2x³ - 5x +3

P = Finding the divisors of the constant 3 : 1 and 3
Q = Finding the divisors of the master coefficient 2 : 1 and 2

Now verify the probably roots: +- p/q
+- 1/1 , +-1/2 , +-3/1 , +-3/2

+-1 , +-1/2 , +-3    , +- 3/2

x=1 is root: 2x³-5x+3 = 2(1)³-5(1)+3 = 0

If x=1 is root, so x-1=0

Divinding by (x-1)

2x³+0x²-5x+3 | x-1
-2x³+2x² 2x² +2x-3
  0 +2x²-5x
-2x²+2x
0 -3x +3
3x - 3
0 0

So,
2x³-5x+3 = (x-1)(2x²+2x-3)

(x-1)(2x²+2x-3)

Related Questions

What is the answer to 3d+8=2d-17
What is 6.213 as a mixed number
What is the additive inverse of 4x
Compare partial products and regrouping how the methods are alike and different
Which of the following correctly represents the set of numbers using interval notation?

The formula a= bf-v1 is used to calculate acceleration as the change in velocity over a period of time. Solve the formula for the final velocity, bf in terms of initial velocity, v1, acceleration, a, and time,

Answers

Answer:

The formula for the final velocity, bf in terms of initial velocity, v1, acceleration, a, and time is given as

$bf=v1+a* t$

Step-by-step explanation:

Given:

$a=(bf-v1)/(t)$

To Find:

bf = ?

Solution:

Acceleration:

Acceleration is defined as the ratio between the change in velocity of an object and the time it takes for the object to change the velocity.

In formula, this is written as:

$a=(v_(f)-v_(i))/(t)$

Where,

'a' is the Acceleration.

'vf' is the final velocity.

'vi' is the initial velocity.

't' is the time it takes for the object to accelerate from vf to vi

Here it is given as

$a=(bf-v1)/(t)$

So,

Where,

'a' is the Acceleration

'bf' is the final velocity.

'v1' is the initial velocity.

't' is the time it takes for the object to accelerate from bf to v1.

On Solving the above equation 'bf' we get

$a=(bf-v1)/(t)\n\na* t=bf-v1\n\nbf=v1+a* t$ ....As required

Final answer:

In physics, the formula bf = a + v1 is used to calculate the final velocity in terms of the initial velocity, acceleration, and time. If acceleration is zero, final and initial velocities are equal, pointing to constant velocity. If acceleration is negative, the final velocity is less than the initial, indicating deceleration.

Explanation:

The equation a = bf - v1 is used to calculate acceleration, defined as the change in velocity over a period of time. To solve for the final velocity, bf, we simply need to rearrange the equation.

So, bf = a + v1. This equation tells us that the final velocity is equal to the sum of the initial velocity and the acceleration.

Other insights we can gather from this equation include: if acceleration is zero, the final and initial velocities are equal, pointing to constant velocity. This is because there's no change in speed. Conversely, if acceleration is negative, the final velocity is less than the initial, indicating a decrease in speed or deceleration.

Learn more about Final Velocity here:

brainly.com/question/28608160

#SPJ12

What is the length of the line segment that is graphed from (3, 1) to (8, 1)?A.
4 units

B.
5 units

C.
8 units

D.
9 units

Answers

Hello,

all you have to do is to calculate the distance betheen the 2 points (pythagorean theorem)

d²=(3-8)²+(1-1)²=25+0=25

d=5

16. Dilakukan pengukuran volume benda yangberbentuk tabung. Jika jari-jari tabung =
0,40 m dan tinggi tabung = 50 cm, volume
tabung tersebut adalah ....
A. 0,2512 m³
B.
EVC.
C.
D.
2,512 m³
25,12 m³
251,1 m³

Answers

It will be letter A I believe

The line y=mx is tangent to the curve y^2 = X-C. Show that c = 1/ (4m^2)

Answers

Hello,
Let (a,b) the intersection of the tangent and the curve.
That point must be double.

So
b=m*a
b²=a-c
==>(ma)²-a+c=0
==>m²a²-a+c=0 roots must be equal
Δ=(-1)²-4*m²c=0 => 4m²c=1==>c=1/(4m²)

Martin has a combination of 33 quarters and dimes worth a total of $6. Which system of linear equations can be used to find the number of quarters, q, and the number of dimes, d, Martin has?A) q + d = 6
25q + 10d = 33

B) q + d = 6
0.25q + 0.1d = 33

C) q + d = 33
25q + 10d = 6

D) q + d = 33
0.25q + 0.1d = 6

Answers

Answer: D) . $q+d=33$

$0.25q+0.1d=6$

Step-by-step explanation:

We know that $1 = 4 quarters

⇒ 1 quarter = $(1)/(4)=\$0.25$

$1 = 10 dimes

1 dime = $(1)/(10)=\$0.1$

Let 'q' be the number of quarters and 'd' be the number of dimes.

Since, Martin has a combination of 33 quarters and dimes worth a total of $6.

$q+d=33$

$0.25q+0.1d=6$

Answer:

q + d = 33 0.25q + 0.1d = 6

Step-by-step explanation:

I hope I help you.

The table below shows the blood types of 75 donors after a one-day blood drive. Based on the results, what is the chance that a random donor has type A blood..?Blood Type- O A B AB
Frequency- 31 33 9 2

Answers

Based on the results, the chance that a random donor has type A blood is; 11/25

How to find the Probability?

We are told that there was a survey of 75 blood donors.

Now, we want to find the chance that a random donor has type A blood. From the given table, we see that there are 33 type A blood donors. Thus;

P(donor has type A blood) = 33/75 = 11/25

Read more about Probability at; brainly.com/question/251701

#SPJ5

What I think the chance that a random donor has type a blood is 44% because there are 33 people in total of 75 that have type A blood type so you simply just divide 33/75 then get .44 which is 44%

Other Questions

Point T is the midpoint of line AB. If TB=6, find the length of AB?

Write a mixed number that is greater than 12/4 and less than 15/4

Mofor had $21 to spend on two notebooks. After buying them he had $13. How much did each notebook cost?

Which shows the dimensions of two rectangular prisms that have volumes of 72 cm3 but different surface areas? A. 6 cm by 3 cm by 4 cm; 12 cm by 2 cm by 3 cm B. 2 cm by 4 cm by 9 cm; 9 cm by 4 cm by 2 cm C. 3 cm by 3 cm by 8 cm; 2 cm by 6 cm by 8 cm D. 6 cm by 3 cm by 4 cm; 9 cm by 4 cm by 3 cm