3(2) + 24x + 48 = 0 6 + 24x + 48 = 0 24x + 54 = 0 24x + 54 - 54 = 0 - 54 24x = -54 24x/24 = -54/24 x = -9/4 x = -2 1/4
factor the trinomial 16x^2+24x+9
While it is possible to take 4x out of all of those, it is also possible to add them and get 48x, which factors to 2 * 2 * 2 * 2 * 3 * x
3x3-18x2+24x=3x(x2-6x+8)=3x(x-4)(x-2)
24x^3 + 72x2 + 30x = 6x*(4x^2 + 12x + 5)=6x*(2x + 1)*(2x + 5)
4x**3-x**2*24x+6 is an expression, it has no answer however it factors to: (4x-1)(x**2-6)
24x^5 + 24x^3 = 24x^3(x^2 + 1)
12x^2+24x+12 12(x^2+2x+1) 12(x+1)^2
3(2) + 24x + 48 = 0 6 + 24x + 48 = 0 24x + 54 = 0 24x + 54 - 54 = 0 - 54 24x = -54 24x/24 = -54/24 x = -9/4 x = -2 1/4
(24x)^5 - (24x)^3 + (16x)^2 - 16 This can be simplified multiple ways: 1. pull (24x)^3 out of the first two terms and 16 out of the second two. (24x)^3((24x)^2-1) + 16(16x^2-1) 2. just pull 8 out of everything 8(3*(24x)^4-3*(24x)^2+32x^2-2) ...
factor the trinomial 16x^2+24x+9
(x^2) + 24x + 144 = -9 x = -12
While it is possible to take 4x out of all of those, it is also possible to add them and get 48x, which factors to 2 * 2 * 2 * 2 * 3 * x
This may be copied wrong, but as written that equals 4x^2-15x which factors to x(4x - 15)
Let the symbol ^ mean "to the power" Then 9x^2 + 24x + 16 = (3x + 4)(3x +4) = (3x + 4)^2
8x6 + 24x5 + 16x4 = 8x4 ( x2 + 3x + 2) = 8x4 (x + 2) ( x + 1)
-x3 -10x2 + 24x 1) -x can be factored out to give, -x(x2 + 10x - 24) 2) The bracketed expression can be factored as (x + 12)(x - 2), which now gives, -x(x + 12)(x - 2) = -x3 -10x2 + 24x