Answer:
There are many different types of expressions.
To factor expressions with variables, the first thing is to take out any common factors always across all terms.
Ex: 5x + 15
= 5(x + 3)
To factor trinomials with one variable (standard form): [tex]ax^{2} + bx + c = 0[/tex], after taking out the common factor if there is one, you can:
i) Use the quadratic formula. [tex]x = \frac{-b +- \sqrt{b^{2} -4ac} }{2a}[/tex]
ii) Decomposition (factors of a and c multiply and added to give b)
Ex: 2x² - 7x + 3 2 * -3 = -6
(2 -1 ) 1 * -1 = -1
(1 -3 ) -6 + -1 = -7
=(2x-1)(x-3)
Trinomials with two variables like: ax² + bxy + cy² = 0
Use decomposition but include the second variable.
Ex: 2x² - 7xy + 3y² 2 * -3 = -6
(2 -1 ) 1 * -1 = -1
(1 -3 ) -6 + -1 = -7
=(2x-1y)(x-3y)
When a square value is being subtracted from another square value.
Difference of squares: [tex]x^{2} - y^{2}[/tex] = (√x² - √y²)(√x² + √y²)
Ex: 36x² - k²
= (6x - k)(6x + k)
