Write a General Rule for Factoring Quadratics when a=1

Answer 1

ax^2+ bx +c when a =1

This is another way of asking, how to factor or express in factored form from a polynomial.

One of the major rules or driving forces to factoring is coming up with 2: numbers that can be written in parentheses so that when following FOIL or First, Outer, Inner and Last and when like terms are combined they will add up and be expressed in that polynomial form.

So you ask the questions, what 2 numbers (when written in factored form) when multiplied together will have the middle term add up to be that number but yet also at the same time multiply as the last number to be the last term in the sequence of the polynomial.

Here is an example:

(x-6)(x+7)

This is the factored form.

In polynomial form it is:

x^2 + x - 42

Notice how when you follow the FOIL method. The outer and inner, -6x and 7x combine to just make x. The -6 and 7 are multiples to make a negative 42 or -42. The x^2 is the result of multiplying both x's and is the leading term.

Factoring is solving the polynomial in reverse or working it backwards from polynomial form to factored form.

Answer 2

1) Check General Forms

2) FOIL

3) Quadratic Formula