Polynomial f(x) has x-intercepts at x = 2 , x = -2, x = 3 and x = -3. Write the polynomial in factored form and then multiply the factors to produce a polynomial.

Question

anonymous · Answer

If we know the roots of a polynomial are a, b, c, and d, then we know the polynomial is equal to some constant times:
(x-a)(x-b)(x-c)(x-d) and so on. This can be done for any amount of factors. So, in this case, the roots are 2, -2, 3, and -3. So:
(x-2)(x--2)(x-3)(x--3)=(x-2)(x+2)(x-3)(x+3). I'll leave the multiplying out for you to work out. As a hint, try FOILing the first two, and FOILing the last two.

anonymous · Answer

thank youu!!

anonymous · Answer

after i foil the first and last to, do i then foil again?

anonymous · Answer

*last two

anonymous · Answer

oh, i guess i would

anonymous · Answer

Yep. But multiplying the first two followed by the last two is useful because they are the difference of two perfect squares, but in reverse. So the inside and outside terms cancel.