Algebra 1 Flashcards
Variable:
any letter used in algebra and that letter represents a mystery number or unknown. They are called variables because their value can vary or change
Coefficient:
A number or symbol that is multiplying a variable. The coefficient number is usually written in front of the variable
Constant:
a quantity that does not vary or change but stays the same.
Power/index
a small number that is written as a superscript above a variable or number which tells us if that quantity is squared, cubed or raised to the power of 4, or raised to the power of 5 etc
Terms:
a constant, a variable OR a constant multiplied by one or more variables.
Algebra Expression:
must contain one or more numbers, one or more variables, and one or more arithmetic operations
Polynomials:
have variables that ONLY have WHOLE NUMBER powers
Degree of a polynomial:
highest power of the variable
Linear (degree 1)
3x +5
Quadratic (degree 2)
2x² +4x -1
Cubic (degree 3)
4x³ +2x +6
Quartic (degree 4)
5x⁴ -3x² +4x
How to expand products
Square first term
Multiply terms + double the answer
Square last term
(a+b)³
(a+b)³ =a³ +3a²b + 3ab² +b³
power of 5 => ___ terms
6 terms
HCF- Highest Common Factor
Divide by the biggest no. you can
Difference of 2 squares
𝒂²−𝒃²=(𝒂−𝒃)(𝒂+𝒃)
Difference of 2 cubes
a³-b³ = (a-b)(a²+ab+b²)
Sum of 2 cubes
a³+b³ = (a+b)(a²+ab+b²)
Quadratic trinomial
Guide number method
Facrors by grouping
ax-bx+ay-by = (x+y) (a-b)
Guide number method
Multiply 1st term x last term
find a pair of factors that add up to middle term
3x² + 11x -20
(3x20=60, 4x15=60-4+15=11)
3x² -4x +15x -20
3x(x+5) -4(x+5)
When doing anything with fractions
Factorise as much as possible
to add/subtract fractions
Find a common factor
