Question

What is the difference between solving and factoring a quadratic expression like this:
x^2-2x-3=0
compared to one like this:
x^2-11x+24

Also, why is it that you switch the signs of the factored versions of ax^2+bx+c = 0 when factoring? For example, a problem such as:
x^2+ 10x + 9=0
where you have x = -1, -9
Wouldn't it just be x=1,9 because 1+9 = 10 and 1*9 = 9?

Answer 1

factoring can be one of several methods used to solve an equation.

so both quadratics can be factored

\[(x -3)(x + 1) = 0\]


which contains an equals sign.... so to solve it you need

if either factor is zero, then the equation is zero. So find the values of x, that
make the factors equal zero. So you need to solve

x - 3 = 0

and

x +1 = 0

The 2nd one is only an expression, contains no equals signs of inequalities.

all you can do is express it as the product of binomial factors.

\[(x -8)(x-3) \]

hope this helps

Answer 2

there are a few clues in the question when factoring

middle term positive, last term positive both factors are positive

(x +3)(x +2) = x^2 + 5x + 6

middle negative and last positive, both negative

(x -2)(x -4) = x^2 - 6x + 8

middle positive last negative, larger factor is positive

(x + 7)(x -2) = x^2 + 5x - 14

middle negative, last negative, means the larger factor is negative

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

hope this helps

Answer 3

So in other words it doesn't matter if says =0 at the end of each expression or not, it will always =0 even if it doesn't say it at the end of the expression?

Answer 4

well sometimes it ca say something else

like

x^2 + 14x + 57 = 8

rewrite it as

x^2 + 14x + 49 = 0

and now you can factorise..

the solutions affect the graphing of the equation. By setting it equal to zero, you can find where the curve cuts the x-axis.