Write down a set of factors for
and
.
The possible factors for
are: (1,3).
The possible factors for
are: (-1,1) or (1,-1).
Write down a set of options for the possible factors of the quadratic using the factors of
and
.
Therefore, there are two possible options.
Option 1
Option 2
The factors of
are
and
.
Factorising a trinomial
Factorise the following:
(a)
(b)
(c)
(d)
(e)
(f)
Factorise the following:
Find the factors for the following trinomial expressions:
Find the factors for the following trinomials:
Factorisation by grouping
One other method of factorisation involves the use of common factors. We know that the factors of
are 3 and
. Similarly, the factors of
are
and
. Therefore, if we have an expression:
then we can factorise as:
You can see that there is another common factor:
. Therefore, we can now write:
We get this by taking out the
and seeing what is left over. We have a
from the first term and a
from the second term. This is called
factorisation by grouping .
Find the factors of
by grouping
There are no factors that are common to all terms.
7 is a common factor of the first two terms and
is a common factor of the second two terms.
is a common factor.
The factors of
are
and
.
Factorisation by grouping
Factorise by grouping:
Factorise by grouping:
Factorise by grouping:
Factorise by grouping:
Factorise by grouping:
Simplification of fractions
In some cases of simplifying an algebraic expression, the expression will be a fraction. For example,
has a quadratic in the numerator and a binomial in the denominator. You can apply the different factorisation methods to simplify the expression.
If
were 3 then the denominator,
, would be 0 and the fraction undefined.
Simplify:
Use
grouping for numerator and
common factor for denominator in this example.
The simplified answer is:
Simplify:
The simplified answer is
Simplification of fractions
Simplify:
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
(l)
(m)
(n)
(o)
(p)
(q)
(r)
Simplify:
Summary
Product of two binomials
Factorising
Distributive law
Sum and difference of cubes
Factorising quadratics
Factorising by grouping
Simplifying fractions
End of chapter exercises
Factorise:
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
Show that
can be simplified to
What must be added to
to make it equal to
Questions & Answers
A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?