How can I convert ax^{2}+bx+c=0 to a FOIL-style (x+d)(x-e)=0 equation?

blitzbabeiy 2022-01-23 Answered
How can I convert ax2+bx+c=0 to a FOIL-style (x+d)(xe)=0 equation?
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Nevaeh Jensen
Answered 2022-01-24 Author has 14 answers
Rylee Marshall
Answered 2022-01-25 Author has 6 answers
Step 1
If a polynomial has a root r (imaginary or real), then you can pull out a factor of xr.
For example, to factor x2+1, we first find the roots. You can use the quadratic equation for this in general, but it's easy to see in this example that the roots are i and -i. This means the polynomial x2+1 factors as (xi)(x+i).
Notice this polynomial has no real solutions. There is no amount of algebraic trickery you can do to get around that fact. Depending on your application, you will either have to accept the imaginary roots or regard the polynomial as having no (real) solutions.
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RizerMix
Answered 2022-01-27 Author has 438 answers
Step 1ax2+bx+c=a(xb+b24ac2a)(xbb24ac2a)If you plug a number n into a polynomial and get 0, then (xn) is a factor of that polynomial. So the two numbers that you can plug into a quadratic polynomial that mkae it add up to 0 correspond to the two factors. But you can't get real numbers if the solutions are not real numbers.
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