4.2 Faktorisering en breke (Page 2/4)

Siyavula textbooks: wiskunde Page 2 / 4

Daar is sekere wenke wat jy in gedagte kan hou:

As $c$ positief is, moet albei die faktore van $c$ positief of albei negatief wees. Die faktore is beide negatief indien $b$ negatief is, en beide positief indien $b$ positief is. As $c$ negatief is, beteken dit slegs een van die faktore van $c$ is negatief, en die ander een is positief.
Wanneer jy 'n antwoord gekry het, brei weer jou hakies uit net om te toets of dit reg uitwerk.

Vind die faktore van $3 x^{2} + 2 x - 1$ .

Kontroleer of die kwadratiese uitdrukking in die vorm $a x^{2} + b x + c$ is met $a$ positief.
Die kwadraat is in die regte vorm.

Skryf twee hakies neer met 'n

x

in elke hakie en spasie vir die oorblywende terme.

(x) (x)

Skryf die stel faktore neer van $a$ en $c$ . Die moontlike faktore van $a$ is: (1,3). The moontlike faktore van $c$ is: (-1,1) of (1,-1).

Skryf die groep opsies neer van die moontlike faktore van die kwadratiese uitdrukking $a$ en $c$ . Daar is twee moontlike oplossings.

Opsie 1	Opsie 2
$(x - 1) (3 x + 1)$	$(x + 1) (3 x - 1)$
$3 x^{2} - 2 x - 1$	$3 x^{2} + 2 x - 1$

Kontroleer jou antwoord
$\begin{matrix} (x + 1) (3 x - 1) & = & x (3 x - 1) + 1 (3 x - 1) \\ = & (x) (3 x) + (x) (- 1) + (1) (3 x) + (1) (- 1) \\ = & 3 x^{2} - x + 3 x - 1 \\ = & x^{2} + 2 x - 1 . \end{matrix}$
Skryf die finale antwoord neer
Die faktore van $3 x^{2} + 2 x - 1$ is $(x + 1)$ en $(3 x - 1)$ .

Faktorisering van 'n kwadratiese drieterm

Faktoriseer die volgende:

(a) $x^{2} + 8 x + 15$	(b) $x^{2} + 10 x + 24$	(c) $x^{2} + 9 x + 8$
(d) $x^{2} + 9 x + 14$	(e) $x^{2} + 15 x + 36$	(f) $x^{2} + 12 x + 36$

Ontbind die volgende in faktore:
1. $x^{2} - 2 x - 15$
2. $x^{2} + 2 x - 3$
3. $x^{2} + 2 x - 8$
4. $x^{2} + x - 20$
5. $x^{2} - x - 20$
Vind die faktore van die volgende drieterme:
1. $2 x^{2} + 11 x + 5$
2. $3 x^{2} + 19 x + 6$
3. $6 x^{2} + 7 x + 2$
4. $12 x^{2} + 8 x + 1$
5. $8 x^{2} + 6 x + 1$
Faktoriseer die volgende drieterme:
1. $3 x^{2} + 17 x - 6$
2. $7 x^{2} - 6 x - 1$
3. $8 x^{2} - 6 x + 1$
4. $2 x^{2} - 5 x - 3$

Faktorisering deur groepering

'n Verdere metode van faktorisering gebruik gemeenskaplike faktore. Ons weet dat die faktore van $3 x + 3$ , 3 en $(x + 1)$ is. Soortelyk is die faktore van $2 x^{2} + 2 x$ , $2 x$ en $(x + 1)$ . Gevolglik het ons 'n uitdrukking:

2 x^{2} + 2 x + 3 x + 3

wat ons kan faktoriseer as:

2 x (x + 1) + 3 (x + 1)

Nou kan ons sien daar is 'n ander gemene faktor: $x + 1$ . Gevolglik kan ons nou skryf:

(x + 1) (2 x + 3)

Ons kry dit deur die $x + 1$ 'uit te haal' (uit te deel) en te sien wat oorbly. Ons het $+ 2 x$ uit die eerste term en $+ 3$ uit die tweede term. Dit word genoem faktorisering deur groepering .

Vind die faktore van $7 x + 14 y + b x + 2 b y$ deur groepering

Bepaal of daar faktore is wat gemeenskaplik is aan al die terme
Daar is geen algemene gemeenskaplike faktore nie.
Bepaal of daar faktore is wat gemeenskaplik is in sommige van die terme
7 is 'n gemene faktor van die eerste twee terme en $b$ is 'n gemene faktor van die tweede twee terme.
Herskryf die uitdrukking met inagneming van die faktore
$7 x + 14 y + b x + 2 b y = 7 (x + 2 y) + b (x + 2 y)$
Bepaal of daar verdere gemeenskaplike faktore is
$x + 2 y$ is 'n gemeenskaplike faktor.
Herskryf die uitdrukking in faktorvorm
$7 (x + 2 y) + b (x + 2 y) = (x + 2 y) (7 + b)$
Skryf die finale antwoord neer
Die faktore van $7 x + 14 y + b x + 2 b y$ is $(7 + b)$ en $(x + 2 y)$

Khan akademie video oor faktorisering van 'n drieterm deur groepering

Faktorisering deur groepering

Faktoriseer deur groepering: $6 x + a + 2 a x + 3$
Faktoriseer deur groepering: $x^{2} - 6 x + 5 x - 30$
Faktoriseer deur groepering: $5 x + 10 y - a x - 2 a y$
Faktoriseer deur groepering: $a^{2} - 2 a - a x + 2 x$
Faktoriseer deur groepering: $5 x y - 3 y + 10 x - 6$

Questions & Answers

Three charges q_{1}=+3\mu C, q_{2}=+6\mu C and q_{3}=+8\mu C are located at (2,0)m (0,0)m and (0,3) coordinates respectively. Find the magnitude and direction acted upon q_{2} by the two other charges.Draw the correct graphical illustration of the problem above showing the direction of all forces.

Kate Reply

To solve this problem, we need to first find the net force acting on charge q_{2}. The magnitude of the force exerted by q_{1} on q_{2} is given by F=\frac{kq_{1}q_{2}}{r^{2}} where k is the Coulomb constant, q_{1} and q_{2} are the charges of the particles, and r is the distance between them.

Muhammed

What is the direction and net electric force on q_{1}= 5µC located at (0,4)r due to charges q_{2}=7mu located at (0,0)m and q_{3}=3\mu C located at (4,0)m?

Kate Reply

what is the change in momentum of a body?

Eunice Reply

what is a capacitor?

Raymond Reply

Capacitor is a separation of opposite charges using an insulator of very small dimension between them. Capacitor is used for allowing an AC (alternating current) to pass while a DC (direct current) is blocked.

Gautam

A motor travelling at 72km/m on sighting a stop sign applying the breaks such that under constant deaccelerate in the meters of 50 metres what is the magnitude of the accelerate

Maria Reply

please solve

Sharon

8m/s²

Aishat

What is Thermodynamics

Muordit

velocity can be 72 km/h in question. 72 km/h=20 m/s, v^2=2.a.x , 20^2=2.a.50, a=4 m/s^2.

Mehmet

A boat travels due east at a speed of 40meter per seconds across a river flowing due south at 30meter per seconds. what is the resultant speed of the boat

Saheed Reply

50 m/s due south east

Someone

which has a higher temperature, 1cup of boiling water or 1teapot of boiling water which can transfer more heat 1cup of boiling water or 1 teapot of boiling water explain your . answer

Ramon Reply

I believe temperature being an intensive property does not change for any amount of boiling water whereas heat being an extensive property changes with amount/size of the system.

Someone

Scratch that

Someone

temperature for any amount of water to boil at ntp is 100⁰C (it is a state function and and intensive property) and it depends both will give same amount of heat because the surface available for heat transfer is greater in case of the kettle as well as the heat stored in it but if you talk.....

Someone

about the amount of heat stored in the system then in that case since the mass of water in the kettle is greater so more energy is required to raise the temperature b/c more molecules of water are present in the kettle

Someone

definitely of physics

Haryormhidey Reply

how many start and codon

Esrael Reply

what is field

Felix Reply

physics, biology and chemistry this is my Field

ALIYU

field is a region of space under the influence of some physical properties

Collete

what is ogarnic chemistry

WISDOM Reply

determine the slope giving that 3y+ 2x-14=0

WISDOM

Another formula for Acceleration

Belty Reply

a=v/t. a=f/m a

IHUMA

innocent

Adah

pratica A on solution of hydro chloric acid,B is a solution containing 0.5000 mole ofsodium chlorid per dm³,put A in the burret and titrate 20.00 or 25.00cm³ portion of B using melting orange as the indicator. record the deside of your burret tabulate the burret reading and calculate the average volume of acid used?

Nassze Reply

how do lnternal energy measures

Esrael

Two bodies attract each other electrically. Do they both have to be charged? Answer the same question if the bodies repel one another.

JALLAH Reply

No. According to Isac Newtons law. this two bodies maybe you and the wall beside you. Attracting depends on the mass och each body and distance between them.

Dlovan

Are you really asking if two bodies have to be charged to be influenced by Coulombs Law?

Robert

like charges repel while unlike charges atttact

Raymond

What is specific heat capacity

Destiny Reply

Specific heat capacity is a measure of the amount of energy required to raise the temperature of a substance by one degree Celsius (or Kelvin). It is measured in Joules per kilogram per degree Celsius (J/kg°C).

AI-Robot

specific heat capacity is the amount of energy needed to raise the temperature of a substance by one degree Celsius or kelvin

ROKEEB

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Source: OpenStax, Siyavula textbooks: wiskunde (graad 10) [caps]. OpenStax CNX. Aug 04, 2011 Download for free at http://cnx.org/content/col11328/1.4

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