Question

please help on how to FOIL after you find the answer to a factoring question.I also don't know what factoring method to use while looking at an equation. Can I just use the long MA table all the time ? example:4x^2+19x-5

Answer 1

No need to bother with foil
expanding factors is easy - use the distributive law

(x + 2)((x - 3)
= x(x - 3) + 2(x - 3)
= x^2 - 3x + 2x - 6 = x^2 - x - 6

just multiply the second parentheses by 3 then by +2

Answer 2

* multiply the second parentheses by x ( not 3!)

Answer 3

The factoring method depends on your situation.
For quadratic trinomials (3 terms) there are two ways

4x^2+19x-5
First|middle |last

1) The first involves finding two numbers that multiply to make the PRODUCT of the first and last term (i.e. the coefficient of x^2 and the constant) AND SUM to give the middle term (coefficient of x).

P: first x last term: 4 x - 5 = -20
S = 19

So we need two numbers that multiply to make -20 and also add to 19.
-1 and 20 are the two numbers we need.

Once you have these two numbers you can SPLIT the middle term (19x) into terms with these two as coefficients.

So 4x^2+19x-5 becomes 4x^2+20x - x -5
Then group in pairs and factorise

4x^2+20x - x -5 = 4x(x+5) - (x+5) = (4x-1)(x+5)

An alternative approach is to use boxes once you have figured out the two special numbers.