(y-2) (x + 3) are factors of the xy + 3y-2x-6 form
Further explanation
Factoring is a statement of a form of addition into a multiplication
There are several factoring of the following forms:
- 1. the forms ax + ay + az and ax + bx -cx
factoring:
ax + ay + az = a (x + y + z + ...)
ax + bx -cx = x (a + b-c)
- 2. difference of two squares x²-y²
factoring:
x²-y² = (x-y) (x + y)
- 3. the form x² + 2xy + y² and x²-2xy + y²
factoring:
x² + 2xy + y² = (x + y) (x + y) = (x + y)²
x²-2xy + y² = (x-y) (x-y) = (x-y)²
- 4. form ax² + bx + c with a = 1
factoring:
ax² + bx + c = (x + m) (x + n) with m x n = c and m + n = b
- 5. the form ax² + bx + c with a ≠1 and a ≠0
factoring:
can be completed in 2 ways
a. distributive way
ax² + bx + c = ax² + px + qx + c with
p x q = a x c and
p + q = b
b. formula way
ax² + bx + c = 1/a (ax + m) (ax + n) with
m x n = a x c and
m + n = b
So from an addition form, for example:
ax + ay = a (x + y), then a and (x + y) are factors of the form ax + ay
So (y-2) (x + 3) are factors of the form xy + 3y-2x-6
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Keywords: factoring, quadratic equation, addition into a multiplication
