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
To multiply fractions
Top by top, bottom by bottom
To divide fractions
Invert (flip) the second fraction and multiply
Algebraic fractions with fractions
Multiply each term by LCM
Binomial expansions
Use choose function
Another word for answer
quotient
Divisor is
the number being divided by
dividend is
the number getting divided
long division with algrebra
Divide first term of dividend by first term of divisor
multiply answer by the divisor
change signs
bring down next sign
repeat
If you are dividing 2x³ +13x² -36, what do you need to insert
Insert a 0x between 13x² and -36
If you get a remainder, is it a factor?
NO
