solving expanding quadratic equations is easy if you use the distributive property to expand binomials. Collect like terms to simplify.
example 1 : ( x + 4 ) ( x – 2 )= x2 – 2x + 4x – 8
= x2 + 2x – 8
example 2: ( x + 5 )2
= ( x + 5 ) ( x + 5 )
= x2 + 10x + 25
example 3 :( x – 3 ) ( x + 3 )= x2 – 3x + 3x – 9
= x2 – 9
Factoring is the opposite of expanding. If every term of a polynomial is divisible by the same constant, the constant is called a common factor. A polynomial is not considered to be completely factored until the greatest common factor (G.C.F. ) has been factored out.
For factoring with trinomials you just have to find two numbers whose product should give you C and added those numbers should give you B. factoring trinomial form is
Standard Form: ax^2+ bx + c
Factoring when a is not 1 is simple all you have to do is
1: Multiple a by c
2: Find factors of new number
(find two numbers multiplied together to get c and added together to get b)
3: Write in standard form, using the original a and c value
4: Group and find common factors
5: Place in factor form: (x ) (x )
word problem example
when does the driver hit the water?
complete the square
complete the square is when we take ax^2+bx+c=0 and turn it into a(x+d)^2+e=0. Completing the square is often used to figure out a vertex of a parabola.
- Block out the first 2 terms
- Factor out the "a" value (which comes from standard form which we talked about earlier)
- Take half of the x-term coefficient and square it.
- keep the positive number and take out the negative from the bracket
- Middle value is divided by 2 and then the entire bracket is squared.