Question #ec66c

2 Answers
Oct 26, 2016

On R you can't.

Explanation:

If you can write it as product of 1 degree factors it should be
P(x)=a(x-x_1)(x-x_2)
where x_1 and x_2 are roots of P(x), but if you try to solve the second degrre equation you will find
Delta/4=8^2-3*24=-8<0
so there are no roots on R.

Oct 26, 2016

Complete the square or use the quadratic formula to find the roots, then find the factors.

Explanation:

3x^2-16x+24 = 0 has solutions

x = (8+-2sqrt2i)/3

So

x-(8+2sqrt2i)/3, and x-(8-2sqrt2i)/3 are factors of the quadratic.

In order to get leading coefficient 3, we need a constant factor of 3.

So

3x^2-16x+24 = 3(x-(8+2sqrt2i)/3)(x-(8-2sqrt2i)/3)

If you want strict standard for for the imaginaries, write

3x^2-16x+24 = 3(x-(8/3+(2sqrt2)/3i))(x-(8/3-(2sqrt2)/3i))