Polynomials Flashcards
Polynomial
Expression in the form ax^5 + bx^4 + cx^3 etc..
Expression in the form ax^5 + bx^4 + cx^3 etc..
Polynomial
Coefficient
No. in front of a certain variable
No. in front of a certain variable
Coefficient
Two things to remember when writing polynomials
You do not require all the powers
Powers must be written in descending order
What is a root of a polynomial function
a value of x that makes f(x) = 0
Factorise 5x^3 - 10x
5x (x^2 - 2)
Factorise 9x^2 - 16
(3x - 4) (3x + 4)
Factorise 6x^2 - 7x - 5
(2x + 1) (3x - 5)
Find the roots of 3x^2 - 12 = 0
2 and -2
Value of x^4 - 5x^3 + 6x + 3 when x = -3
Value of a missing power
0
Quotient
Product of division
Product of division
Quotient
Remainder
Number left from division
Number left from division
Remainder
Divisor
Number you are dividing by
Number you are dividing by
Divisor
Quotient divisor remainder original relationship
Original = divisor x quotient + remainder
Method for synthetic division
- Draw L shape and write down coefficients
- Set divisor = 0 and find value
- Divide
- Write down quotient and remainder
- Draw L shape and write down coefficients
- Set divisor = 0 and find value
- Divide
- Write down quotient and remainder
Method for synthetic division
Factor
Number that divides a given number exactly and does not leave a remainder
Number that divides a given number exactly and does not leave a remainder
Factor
What does it mean if f(h) = 0
(x - h) is a factor of f(x)
x=-1
x=2
x=3
x = 3
x = 3/2
x = -3
p = 3
a = 5, b = -22
Factorise 2x^2 - 3x - 2
(2x + 1) (x - 2)
Factorise 3x^2 + 8x - 3
(x + 3) (3x - 1)
Solve 4x^2 - 4x - 3
(2x - 3) (2x + 1)
