Question

how do you factor poly nomials (mostly 2-3 terms) with a coefficent of x squared

Answer 1

Given
ax^2 + bx + c
Goal is to find factors of ac which add up to b, call them p,q
p*q = ac
p+q = b

Example:
3x^2 +10x -8
a=3, b=10, c= -8
ac = 3*-8 = -24
what factors of -24 add up to 10
try 6 and -4
6-4 = 2 (Doesnt work)
try 12 and -2
12-2 = 10 (Works)

Replace 10x with 12x-2x
(3x^2 +12x)+( -2x -8)
3x(x+4) -2(x+4)
(x+4)(3x-2)

Answer 2

Very simple one...

x^2 + 2x + 1

You want the answer in the form of (x + a)(x + b).

Now to find a and b.

Start with the constant (1).

What 2 numbers times to give +1?
+1, +1, or -1, -1

Now look at the number infront of the x, what pluses to give +2 out of the above numbers?
+1 and +1

therefore a = +1 and b = +1

It factorises to (x+1)(x+1).

Gets slightly more complicated when there is a number infront of the x^2.

Or you can just use \[-b \pm \sqrt{b^{2} - 4ac}\over2a\]