P6 + 40p3q + 400q2 = (p3 + 20q)2
Just as a minor point of correction, it is an expression being factorised, not an equation.
Two is a prime factor of that equation.
There is no equation. An equation is true, whereas the statement ( 5 + 7 = -12 ) is false.
35x2 - 38x + 8
That is the most simplifiable version of this equation.
First factor is x, but we need to know the sign of 5x in your equation...
Doesn't factor evenly, use quadratic equation
(x - 4)(2x + 3)
It can't be factored because its discriminant is less than zero.
28w2 + 196wd + 343d2 = 7(2w + 7d)2.
The first equation factors to (3x + 2)(3x + 4) The second equation factors to (3a + 2b)(3a + 4b)
a2 + 12a + 27 = (a + 3)(a + 9)
The discriminant is less than 0 so the equation has no real roots and therefore, no real factors.