Limx→0 [ 1 / (x - 4) + 1 / (x + 4) ] / x = Limx→0 1 / (x2 - 4x) + 1 / (x2 + 4x) = Limx→0 (x2 + 4x) / (x4 - 16x2) + (x2 - 4x) / (x4 - 16x2) = Limx→0 (x2 + 4x - 4x + x2) / (x4 - 16x2) = Limx→0 2x2 / (x4 - 16x2) = Limx→0 2 / (x2 - 16) = 2 / (0 - 16) = -1/8
16x2 + 40x + 25 = 16x2 + 20x + 20x + 25 = 4x(4x + 5) + 5(4x + 5) = (4x + 5)(4x + 5) = (4x + 5)2
yes
sqrt(10x)*sqrt(8x) = sqrt(80x2) = sqrt(16x2*5) = sqrt(16x2)*sqrt(5) = 4x*sqrt(5)
The GCF is xyz2
-16x2 + x + 8 = -1/64(32x - 1 - √513)(32x - 1 + √513)
16x2 + 8x + 1 = 0 : This factorises to (4x + 1)(4x + 1) = 0 When 4x + 1 = 0 then 4x = -1 : x = -1/4.
4X = 16X2 4X - 16X2 = 0 (1 - 4X)4X = 0 ------------------ as you see X = 0 -------- 1 - 4X = 0 - 4X = - 1 X = 1/4 ----------- So, X = 0 and X = 1/4. You check.
(4x+1)(4x-3)
(4x - 3)(4x - 1)
It is: 4-16x2 = (2-4x)(2+4x) when factored
16x2 + 8x + 1 - 9y2 = (4x + 1)2 - (3y)2 which is a difference of two squares. = (4x + 1 + 3y)*(4x + 1 - 3y)
Limx→0 [ 1 / (x - 4) + 1 / (x + 4) ] / x = Limx→0 1 / (x2 - 4x) + 1 / (x2 + 4x) = Limx→0 (x2 + 4x) / (x4 - 16x2) + (x2 - 4x) / (x4 - 16x2) = Limx→0 (x2 + 4x - 4x + x2) / (x4 - 16x2) = Limx→0 2x2 / (x4 - 16x2) = Limx→0 2 / (x2 - 16) = 2 / (0 - 16) = -1/8
You can use the quadratic formula for this.
16x2 - 25 = (4x + 5) ( 4x - 5)
16x2 - 56x + 49 = (4x - 7)2
16x2 - 49 = 42x2 - 72 = (4x)2 - 72 = (4x - 7)(4x + 7)