B+6
(x - a) + (x - a) + (b) = 2 (x - a) + (b) = x - a + x - a + b = 2x - 2a + b
x^2-8x+3 This expression cannot be factored as (x+a)(x+b) where a and b are integers. This is because you cannot find two integers such that their sum is -8 and product 3.
5
11+(7-3)2=
(a x b)^b =ab x b^2 =ab^3
(x - a) + (x - a) + (b) = 2 (x - a) + (b) = x - a + x - a + b = 2x - 2a + b
7.5
3a+ax+3b+bx = 3(a+b)+(a+b)x = (a+b)(3+x)
Use a^3 + b^3 = (a + b)(a^2 - ab + b^2), where a^2 is a squared, a^3 is a cubed. Note that 216 = 6^3.
I am used to going the other way. We will try this. (3,1) = vertex. (X - 3)^2 + 1 = 0 X^2 - 6X + 9 + 1 = 0 X^2 - 6X + 10 = 0 b = -6 c = 10
x + x + 1 + x + 2 + x + 3 = -144x + 6 = 144x = 8x = 2
2x - 13x + 42 = x +ax + b a + b = 2(x - 6.5x + 21) = 34 = a + b
x*2 - 6x + 9 x*2 -3x -3x +9 x(x-3) -3(x-3) (x-3)(x-3) Note also that x*2 - 6x + 9 is of the form a*2 -2ab + b*2 and so the factors are (x-3) and (x-3)
factor b(x+2) + c(x+2) (b+c)(x+2) need more info for futher analysis.
x^3 + ax + 3a + 3x^2 = (x^3 + 3x^2) + (ax + 3a) = x^2(x + 3) + a(x + 3) = (x + 3)(x^2 + a)
Factor them. 2 x 2 x b x b = 4b2 2 x 3 x b x b x b = 6b3 Combine the factors, eliminating duplicates. 2 x 2 x 3 x b x b x b = 12b3, the LCM
(x-2)(x^2+3)