How do you know if it's possible to factorise a quadratic expression?

Answer 1

ax^2 + bx + c = 0

you must find out ax^2 * c value = acx^2

now you must find out the factors for acx^2
select the factors from the list of factors you get.
let the factors be u and v i.e., u * v = acx^2
and u + v = bx
if non of the factors when added equals to the middle term of the equation i.e., bx then then it is not possible to factorise the quadratic equation. So, you will have to use the formula x = - b +or - sqrt {( b^2 - 4ac)/2a

for example:

x^2 + 5x + 6 = 0

x^2 * 6 = 6x^2
factors for 6x^2
3x , 2x
6x,1x

so select 3x, 2x

3x * 2x = 6x^2
and 3x + 2x = 5x

therefore,
x^2 + 5x + 6 = 0
x^2 + 3x + 2x + 6 = 0
x(x + 3) + 2(x + 3) = 0
x + 2 = 0
x = -2
or
x + 3 = 0
x = -3

2x^2 + 4x + 1 = 0

2x^2 * 1 = 2x^2

factors of 2x^2

2x , 1x

and 2x + 1x = 3x and 2x - 1x = x and both these values does not match with the middle term of the equation,
so we must use the formula x = -b + or - sqrt { (b^2 - 4ac)/2a}

a = 2, b = 4, c = 1

substitute them in the formula and find the values of x

Answer 2

Factorise Quadratic

Answer 3

You don't
You just have to try to factorise it and if you can't then use the formula/complete the square.
All these comments about b^2-4ac is about the discriminant, which tells you whether there are real, equal or no real roots to a quadratic equation, but will not tell you if you can factorise it or if you have to solve it another way.

Answer 4

assuming this is in all in the real plane.


By working out the value of b^2-4ac , if b^2-4ac >= 0 then the quadratic expression can be factorised. if its smaller than 0, then it cannot be factorised.

the reason for this is in the quadratic formula b^2-4ac is square rooted, if it is negative then there is no value (in the real space anyway).

Answer 5

Given a quadratic in the form ax^2 + bx + c = 0, it is factorable if you can find factors of (a)*(c) that add to give b.

For example...x^2 - 3x - 2 = 0...

a = 1
b = -3
c = -2

(a)*(c) = (1)(-2) = -2

So you need to find factors of -2 that add to give -3. This would be -2 and -1. So the equation is factorables as (x - 2)(x - 1) = 0.

You can also try the Quadratic Formula and other factoring techniques such as factoring by grouping. In some cases it won't be obvious and you'll need to try to find factors in order to determine if the entire expression is factorable.

Answer 6

To know if a quadratic expression in the form of ax^2+bx+c may ordinarily factorised or not,you must guess if the product of a and c can be converted into two factors whose sum is equal to b
you should be careful about the positive or negative signs of the coefficients .If c is positive,we are sure that both the factors are either positive or negative.To find out and be sure if they are both positive or negative,you should take into consideration the sign of "b".If it is + then both the factors are positive>if howvr,it is "-",both the factors are negative.
What happens if c is negative?It indicates that one of the factor is positive and the other one is negative.Go back again to the signof "B".if it is positive then the larger factor is positive and the smaller factor is negative.however if 'b' is negtive,you may be sure that the largr factor is negative and the smaller of the factors is positive

Answer 7

You can always factorize a quadratic expression with the Quadratic formula. Sometimes you might end up with quadratic roots.

Quadratic Formula:
(-b ± √b² - 4ac)/ 2a

Answer 8

You can factorise ax²+bx+c over the rationals
if and only if b²-4ac is a square.
That follows from the quadratic formula
because that means ax²+bx+c = 0
has rational roots r1 and r2,
so its factors are x-r1 and x-r2.
Example: x²-3x+2.
Here b²-4ac = 1, so we can factorise the expression.

Answer 9

The discriminant in the quadratic formula : D = b² − 4ac ,

from P(x) = ax² + bx + c , shows that

when D > 0 , P(x) has two distinct real roots ,

when D = 0 , P(x) has two coincident real roots , and

when D < 0 , P(x) has no real roots .

Answer 10

Well, generally we don't know a quadratic equation can be factorized by looking at it. You have no choice. You need to do 'trail and error'.