Question
How do you factor a polynomial?
Using the FOIL method works with some simple polynomials. FOIL stands for First, Outside, Inside, Last.
For example:
x^2-4x+4 factors to
(x-2)(x-2)
Check your work by multiplying them all. x times x is first, x times -2 is outside, -2 times x is inside, and -2 times -2 is last. Add the terms to get x^2-2x-2x+4 or x^2-4x+4
In the blank equation, (x+a)(x+b), we see that for this type of polynomial ax and bx have to add to make the middle term and a and b have to multiply to equal the final term. Just pick numbers which suit these conditions. It's easy with practice. Difficult to show.
Using the FOIL method works with some simple polynomials. FOIL stands for First, Outside, Inside, Last.
For example:
x^2-4x+4 factors to
(x-2)(x-2)
Check your work by multiplying them all. x times x is first, x times -2 is outside, -2 times x is inside, and -2 times -2 is last. Add the terms to get x^2-2x-2x+4 or x^2-4x+4
In the blank equation, (x+a)(x+b), we see that for this type of polynomial ax and bx have to add to make the middle term and a and b have to multiply to equal the final term. Just pick numbers which suit these conditions. It's easy with practice. Difficult to show.