Explain how to factor the following triomials forms..
x^2+bx+c and ax^2+bx+c.Is there more than one way to factor this

Question

Explain how to factor the following triomials forms..
x^2+bx+c and ax^2+bx+c.Is there more than one way to factor this

anonymous · Answer

i think if values of a,b and c are not known we cant make a factor

anonymous · Answer

You can. The quadratic formula is the factoring you're looking for. It's usually expressed as a solution for x rather than as a factor. To solve for the factors, you'll need to know how to complete the square.

Factoring is unique. So, there may be multiple ways to arrive at the solution, but the factors themselves are unique.

anonymous · Answer

There is a general way to factor ax^2+bx+c (if it is factorable; if not it is 'prime').
For x^2+bx+c, when a=1, there is a short cut.

@DanielxAK the quadratic formula does not factor quadratic trinomials, it solves the equation ax^2+bx+c=0. It is the same as completing the square.
It can be used to solve quadratics that are not factorable, but is not the same as factoring.

anonymous · Answer

General method:
Assume
$$ax^2+bx+c = (px+m)(qx+n) : $$
$$p \cdot q =a$$
$$p \cdot n + m \cdot q = b$$
$$m \cdot n =c$$
Find two numbers, u and v such that

$$u \cdot v = a \cdot c, \space and \space u+v=b $$
$$ax^2+bx+c = ax^2+ux+vx+c$$
$$ax^2+ux+vx+c = pqx^2+(np+mq)x+mn$$