4ac + 2ad + 2bc +bd = 2a*(2c + d) + b*(2c + d) = (2c + d)*(2a + b)
(2a + b)(2c + d).
It cannot be factored because the discriminant of b2-4ac is less than zero.
Full equation is (-b +/- sqrt(b2 - 4ac))/2a. Try it with x2 - 2x - 3, where a = 1, b = -2 and c = -3...
Discriminant = (b2-4ac) = (25 - 4x2x3) = 1
(2a + b)(2c + d)
4ac + 2ad + 2bc +bd = 2a*(2c + d) + b*(2c + d) = (2c + d)*(2a + b)
(2a + b)(2c + d).
ac + 2ad + 2bc + 4bd = a(c + 2d) + 2b(c + 2d) = (a + 2b)(c + 2d) Now expand to confirm your answer: c(a + 2b) + 2d(a + 2b) = ac + 2bc + 2ad + 4bd ≡ ac + 2ad + 2bc + 4bd
(2a + b)(2c + d)
It cannot be factored because the discriminant of b2-4ac is less than zero.
3x^2+48x+192=3(x^2+16x+62). You can factor the part in the parentheses using the quadratic formula: x= (-b[+-]Sqrt[b^2-4ac])/(2a).
x = (-b (+/-) root( b2 - 4ac)) / 2a Sorry about the messy answer, there are no square root symbols or plus-minus symbols. Here is the proof - ax2 + bx + c = 0 --------> multiply by 4a 4a2x2 + 4abx + 4ac = 0 4a2x2 + 4abx = -4ac ----------> add b2 to both sides 4a2x2 + 4abx + b2 = b2 - 4ac -----------> factorise LHS (2ax + b)2 = b2 - 4ac 2ax + b = (+/-) root( b2 - 4ac) 2ax = -b (+/-) root( b2 - 4ac) x = (-b (+/-) root( b2 - 4ac)) / 2a Maths works people.
This is a basic quadratic function. The easiest way to go about this is by using the quadratic formula.a=5 ; b=20 ; c=20-b + or - root (b2-4ac) all over 2a.
Full equation is (-b +/- sqrt(b2 - 4ac))/2a. Try it with x2 - 2x - 3, where a = 1, b = -2 and c = -3...
Discriminant = (b2-4ac) = (25 - 4x2x3) = 1
X^2 + 7X + 18 = 0 try the discriminant b^2 - 4ac 7^2 - 4(1)(18) 49 - 72 < 0 so, no real roots and no factors of 18 add to 7