Quadratic
How would you factor
x2+5x+6?
(x+2)(x+3)
Explanation:
Factor the quadratic
What two numbers multiply to 6 and add to 5?
2*3= 6
2+3= 5
Perfect! We can factor the quadratic
(x+2)(x+3)= 0
We solved the quadratic by factoring. We looked for two numbers that multiply to 6 and add to 5, which are 2 and 3.
How would you factor
x3-8?
x3 - 8 = (x - 2)(x2 +2x + 4)
Explanation: Difference of cubes formula: a3 - b3 =(a - b)(a2 + ab + b2)
x3 is a cube (a = x)
8 = 23 (b = 2)
so we write:
x3 - 23 = 0
Apply a = x and b = 2:
x3 - 23 = (x - 2)(x2 + 2x +4)
Write in factored form:
x3 - 8 = (x - 2)(x2 +2x + 4)
That's factored form!
How would you factor
X2 - 9?
(x+3)(x-3)
Explanation:
x2-b2 can be factored as (x+b)(x-b)
32=9
x2-32=(x+3)(x-3)
How would you factor
2x3-3x2+18x-27?
(2x-3)(y2+9)
Explanation: Group the first two terms and the last two terms (2x3-3x2)(18x-27)
Factor out GCF: x2(2x-3) + 9(2x-3)
Common binomial is (2x-3)
Factor (2x-3) (x2+9)