Question

-QUICKLY ANSWER PLEASE- How do I factor expressions with variables?

Answer 1

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): $ax^{2} + bx + c = 0$, after taking out the common factor if there is one, you can:

i) Use the quadratic formula. $x = \frac{-b +- \sqrt{b^{2} -4ac} }{2a}$

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: $x^{2} - y^{2}$ = (√x² - √y²)(√x² + √y²)

Ex: 36x² - k²

= (6x - k)(6x + k)