Contains notes on the foundational algebraic ideas for algebra throughout high school. these notes contain all the algebra that should be known by the end of grade 9. contains detailed explanations of processes such as expanding and simplifying polynomials. It also contains practice equations along...
Terminology:
Polynomial : An algebraic expression / equation formed with variables, exponents, and
coefficients together with operations and an equal sign.
Binomial : an algebraic expression with two terms.
Trinomial : An algebraic expression with three terms.
Important to remember:
Anything to the power of 0 is equal to one (except 0⁰, which is undefined)
The degree of a polynomial is the highest of the degrees of the polynomial's monomials with
non-zero coefficients. (aka, the highest exponent, eg. x² − 4x + 7 the degree = 2)
WORKING WITH EQUATIONS:
Difference of two squares: (also known as DOTS) If two terms can be square rooted and are
being subtracted from one another, create two brackets one with + and the other with -, put the
square root of both terms into the brackets. (eg. x²-16 = (x+4)(x-4) )
Practice Equations: 1) 4x²-64
2) 81y²-16x²
Common Factor: Removing a common factor from an equation. (eg1. 3x²+9x = 3x(x+3) ) (eg2.
25x²y-15xy² = 5xy(5x-3y) )
Practice Equations: 1) 2x²+18x
2) 8xy²z - 24x²yz²
Mixed practice: 12x²-75y² (1. Take out a common factor) = 3(4x² - 25y²) (2.DOTS) =
3(2x+5y)(2x - 5y)
Practice Equations: 1)
Common Bracket: removing/ simplifying an equation with a common bracket. 1 create a bracket
with the terms before the common bracket 2. Create another bracket with the common bracket
(only 1) (eg. 3x(x+4)-x(x+4) = (3x-x)(x+4) )
Practice Equations: 1) 4n(3n+10)-3(2N+10)
2) 17x(5x-1)+(5x-1)
Quadratic Equations: x²+x-2=0 1. Find two numbers that have a product (when you multiply
them together) equal to the constant 2. Ensure that the sum of the two numbers (when you add
them together) is equal to the middle term. 3.Create two brackets beginning with the variable
which is squared and put the two numbers found in 1. and 2. Into the brackets. 4) the values for
x are found if you make each bracket equal zero)
x²+x-2=0 = 1) 2x-1=-2 2) 2-1=1 3) (x+2)(x-1)=0 4) x+2=0 or x-1=0 therefore x=-2 or x=1
Practice Equations: 1) x²+x-6=0
2) x²-7x+12=0
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