A few basic concepts I need help with (1 Viewer)

[RideTheLightnin]

I got this sheet where I need to fill in some facts and formulae, and I'm not to sure on some of them. Here they are

• What are the five methods of factorising?
• What are three steps to simplify algebraic fractions?
• What is the conjugate of a surd?
• Express 2root3 as a complete radical
• In solving inequalities, what special rule do you need to remember?

Thanks in advance

 

[RideTheLightnin]

Oh and i just have a question about the dsicrimant.......
When determining if the roots are rational or irrational, they are only rational if the number is 0 or a square (16,25,36 etc.)? My textbooks seems to think this but it always says that rational numbers are anything in the form p/q so just say if i had 41, why isnt it rational?

Thanks

 

[insert-username]

I got this sheet where I need to fill in some facts and formulae, and I'm not to sure on some of them. Here they are

• What are the five methods of factorising?
• What are three steps to simplify algebraic fractions?
• What is the conjugate of a surd?
• Express 2root3 as a complete radical
• In solving inequalities, what special rule do you need to remember?

Thanks in advance

Express 2root3 as a complete radical

Take the square of two and put it under the square root sign (when you multiply two separate surds, you multiply the numbers under the radical sign and place them under one, i.e. you get √12.


In solving inequalities, what special rule do you need to remember?

When you multiply or divide by a negative number, you need to reverse the inequality sign.


What is the conjugate of a surd?

The conjugate is the same surd but with the opposite addition/subtraction sign, i.e. the conjugate of (√2 + 5) is (√2 - 5)


What are the five methods of factorising?

Factoring in general or factorising quadratics? In general, insert brackets by taking out the highest common factor from each term.


What are three steps to simplify algebraic fractions?

1. Simplify numerator and denominator
2. Factorise top and bottom
3. Cancel common factors top and bottom

Oh and i just have a question about the dsicrimant.......
When determining if the roots are rational or irrational, they are only rational if the number is 0 or a square (16,25,36 etc.)? My textbooks seems to think this but it always says that rational numbers are anything in the form p/q so just say if i had 41, why isnt it rational?

Thanks

When you take the square root of 41, you end up with an irrational number, which you then add or subtract to -b to get your two roots. That's why you end up with irrational roots - you're taking the square root of the discriminant.


I_F

 

[RideTheLightnin]

Thanks man you really helped me out there................I feel really dumb for not knowing them lol

 

[klaw]

What are the five methods of factorising?
1. Take out a constant, e.g., 2x+2=2(x+1)
2. Difference of two squares, e.g. (x²-4)=(x+2)(x-2)
3. Cross method (dunno how to explain it)
4. If quadratic gives you rational numbers, say 2 and 4, then your factors are (x-2) and (x-4)
5. Difference and sum of two cubes

There's probably more.... but this is the wrong approach to maths, maths questions aren't like that... you have to actually apply your knowledge in maths....

 

[香港!]

What are the five methods of factorising?
1. Take out a constant, e.g., 2x+2=2(x+1)
2. Difference of two squares, e.g. (x²-4)=(x+2)(x-2)
3. Cross method (dunno how to explain it)
4. If quadratic gives you rational numbers, say 2 and 4, then your factors are (x-2) and (x-4)
5. Difference and sum of two cubes

There's probably more.... but this is the wrong approach to maths, maths questions aren't like that... you have to actually apply your knowledge in maths....

Here's one which might be nice to know:
(x^n-y^n)=[x-y][x^(n-1)+x^(n-2)y+x^(n-3)y²+...+y^(n-1)]

Also this one but it only works for n being an odd positive integer:
(x^n+y^n)=[x+y][x^(n-1)-x^(n-2)y+x^(n-3)y²-...+y^(n-1)]

 

[insert-username]

Thanks man you really helped me out there................I feel really dumb for not knowing them lol

No problems. But like klaw said, this is not the right way to approach maths. You'll be far better off doing as many questions as you can rather than writing out definitions.


I_F