C1 – Polynomials Summary
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
An expression of the form
n 1
a n x  a n 1 x
n
 an2 x
n2







a n  0 and n is a positive
integer, is called a polynomial of degree n.
Add or subtract polynomials by collecting together like terms. (Terms of
the same degree are ‘like terms’)
The Factor theorem states that if f(a) = 0 for a polynomial f(x) then (x –a) is
a factor of the polynomial f(x).
If a polynomial f(x) is divided by (x + 4) for example
f(x) = (x + 4)(quotient) + remainder
The Remainder theorem states that, when a polynomial f(x) is divided by
(x – a), the remainder is f(a).
Algebraic Division – applying long division to algebra.
When sketching graphs of functions you should consider:
1. the degree of the polynomial function.
2. the intersection points with the axes, when x=0 (intersection with the
y-axis) and when y=0 (intersection with the x-axis).
A translation is a movement in a direction parallel to one or both axes.
y  x  a is a translation of y  x by  a units parallel to the y-axis.
 0 
 where a is a
You can describe these translations by the vectors 
 a
2
An expression of the form
a n x n  a n 1 x n 1  a n  2 x n  2  ...  a 0
 ...  a 0
Where a n , a n 1 ,..., a 0 are real numbers with
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C1 – Polynomials Summary
2
Where a n , a n 1 ,..., a 0 are real numbers with








constant.
a n  0 and n is a positive
integer, is called a polynomial of degree n.
Add or subtract polynomials by collecting together like terms. (Terms of
the same degree are ‘like terms’)
The Factor theorem states that if f(a) = 0 for a polynomial f(x) then (x –a) is
a factor of the polynomial f(x).
If a polynomial f(x) is divided by (x + 4) for example
f(x) = (x + 4)(quotient) + remainder
The Remainder theorem states that, when a polynomial f(x) is divided by
(x – a), the remainder is f(a).
Algebraic Division – applying long division to algebra.
When sketching graphs of functions you should consider:
1. the degree of the polynomial function.
2. the intersection points with the axes, when x=0 (intersection with the
y-axis) and when y=0 (intersection with the x-axis).
A translation is a movement in a direction parallel to one or both axes.
y  x 2  a is a translation of y  x 2 by  a units parallel to the y-axis.
 0 
 where a is a
You can describe these translations by the vectors 
 a
constant.

y  ( x  a) 2 is a translation of y  x 2 by  a units parallel to the x-axis.
 a
 .
You can describe these translations by the vectors 
 0 

y  ( x  a) 2 is a translation of y  x 2 by  a units parallel to the x-axis.
 a
 .
You can describe these translations by the vectors 
 0 

The equation of a circle with radius r and centre (0,0) is given by

The equation of a circle with radius r and centre (0,0) is given by
x y r
2

2
The graph of
( x  a) 2  ( y  b) 2  r is a translation of x 2  y 2  r 2 by
a
  . The centre of the circle is obtained by the
b
coordinates a, b .
the vector
x2  y2  r 2
2

The graph of
( x  a) 2  ( y  b) 2  r is a translation of x 2  y 2  r 2 by
a
  . The centre of the circle is obtained by the
b
coordinates a, b .
the vector