Chapter 7 Algebraic Methods - Year 1 Flashcards
Simplify the following expression?
Explain the core consent of algebraic long division?
You do the first term divided the x term in the denominator
Then you multiply that number by the whole denominator and write it beneath the original numerator
Then subtract the 2 terms
Bring down the next term
Then repeat the steps
What else do you need to consider when doing algebraic long division?
The x terms need to be in descending powers of x
If there is no x term you need to add in 0x
Using algebraic long division how do you know if something is a factor?
When there is a no remainder (=0)
What is the trickiest way you would be asked to write a remainder of a algebraic long division question?
The divided result + (the remainder / the factor divided by)
What does the factor theorem allow us to do?
Check easily for factors of an equation
How does the factor theorem work?
If you have f(x) and f(p) = then (x-p) is a factor.
If (x+p) is a factor then f(-p) will =0
Using the factor theorem, how do you show that x+2 is a factor?
Substitute -2 in for x nd then show that it =0
Using the factor theorem how can you factorise an cubic easily?
Start checking values
Once you find a value that makes the equation =0 reverse the sign and x+p will be your factor
Then use algebraic long division to work out the remainder and then factorise the quadratic sensibly
What is a quick tip of how to find factors of cubics using the factor theorem?
Look at what it ends in. If it ends in 3 then the factor will likely be 3,6 or 9
Etc
Using the factor theorem, what would you substitute into f(x) to show that (2x-1) is a factor?
2x-1=0
x=1/2
1/2
If you are given a cubic with an unknown in it and you are told a factor how do you find the unknown?
Use the factor theorem and substitute the factor in as x (reversed sign) then set the equation =0
Then solve for the unknown
