We can use the fact that any polynomial can be written as a
product of linear factors:
ax^n + bx^(n-1) + ... = a(x - x1)(x -
x2)*....*(x - xn)
x1,x2,x3....,xn are the roots of the
polynomial.
In this case, the polynomial is a quadratic and it could
have 2 roots.
We'll get the roots applying quadratic
formula:
x1 = [-24 + sqrt(24^2 -
4*9*16)]/2*9
x1 = (-24 + sqrt(576 -
576))/18
x1 = -24/18
x1 =
-8/6
x1 = -4/3
x2 =
-4/3
Since the discriminant is zero, the equation has 2 real equal
roots and the factorization will be:
9X^2 + 24X + 16 = 9(x - x1)(x -
x2)
9X^2 + 24X + 16 = 9(x +
4/3)^2
We'll factorize by 1/9:
9X^2 +
24X + 16 = (9/9)(3x + 4)^2
9X^2 + 24X + 16 = (3x +
4)^2
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