X cube-4x + 3x square-12 4X square - 4xy + 4x-2y + y square

X cube-4x + 3x square-12 4X square - 4xy + 4x-2y + y square

X cube-4x + 3x square-12
=x²(x+3)-4(x+3)
=(x+3)(x²-4)
=(x+3)(x+2)(x-2)
4X square - 4xy + 4x-2y + y square
=(2x-y)²+2(2x-y)
=(2x-y)(2x-y+2)

X ^ 3-4x ^ 2 + X + 6 factorization remainder theorem method

x³－4x²＋x＋6
=(x³＋x²)－(5x²－x－6)
=x²(x＋1)－(5x－6)(x＋1)
=(x＋1)(x²－5x＋6)
=(x＋1)(x－2)(x－3)

Factorization: (x-1) (x + 1) (x + 3) (x + 5) + 16

(x + 1) (x-1) (x + 3) (x + 5) + 16 = (x + 1) (x + 3) (x-1) (x + 5) + 16 = (XX + 4x + 3) (XX + 4x-5) + 16 = (XX + 4x) ^ 2-2 (XX + 4x) - 15 + 16 = (XX + 4x) ^ 2-2 (XX + 4x) + 1 = (XX + 4x-1) ^ 2 note: (x + 1) (x + 3) = XX + 4x + 3 (x-1) (x + 5) = XX + 4x-5

For a trapezoid, if the upper bottom is reduced by 4cm, it will become a triangle. The area of the trapezoid will be reduced by 8cm2. If the upper bottom is increased by 4cm, it will become a triangle

The trapezoid area is (a + b) * H / 2
Upper and bottom a = 4
The area of triangle is b * H / 2
(a+b)*h/2-b*h/2=8
a*h/2=8 ,h=4
Now the area of the upper and bottom is increased by 4 to (a + 4 + b) * H / 2
The increased area is (a + 4 + b) * H / 2 - (a + b) * H / 2 = 4H / 2 = 8

Given that the maximum value of quadratic function y = f (x) is 13, and f (3) = f (- 1) = 5, find the value of F (2)

f(3)=f(-1)
So the axis of symmetry is x = (3-1) / 2 = 1
Vertex (1,13)
f(x)=a(x-1)²+13
f(3)=4a+13=5
a=-1/2
f(x)=-1/2(x-1)²+13
So f (2) = - 1 / 2 + 13 = 25 / 2

The top of a granary is a cone. The diameter of the bottom of the cone is 6 and the length of the bus is 4. In order to prevent rain, linoleum should be laid on the top of the granary to calculate the area of the linoleum

πra=3×4×π=12π

Given the ellipse 1 / 2 + y ^ 2 = 1 and a point (0,2) outside the ellipse, the locus equation of the midpoint P of the chord AB is obtained by crossing a straight line with the ellipse at two points a and B

Let a (x1, Y1), B (X2, Y2), the midpoint P (x, y) of AB have: 2x = X1 + x2,2y = Y1 + Y2, X1 ^ 2 / 2 + Y1 ^ 2 = 1, X2 ^ 2 / 2 + Y2 ^ 2 = 1. By subtracting the two formulas, we get: (x1 + x2) (x1-x2) / 2 + (Y1 + Y2) (y1-y2) = 0, that is: 2x (x1-x2) = - 2Y (y1-y2) (y1-y2) / (x1-x2) = - X / y. let a (0,2), then the slope of AP is: k = (y

A triangle and a parallelogram have the same area and height. If the bottom of the triangle is 16 cm, what is the bottom of the parallelogram

A triangle and a parallelogram have the same area and height. If the bottom of the triangle is 16 cm, the bottom of the parallelogram is 8 cm

Prime numbers larger than 2 are a. even. B. odd

B

The length of the bottom edge of an isosceles triangle is 10 cm. The middle line of the waist is drawn from one end of the bottom edge. The circumference of the triangle is divided into two parts. If one part is 4 cm longer than the other part, the waist length of the isosceles triangle is 0______ cm．

According to the meaning of the question, let the waist length of an isosceles triangle be x cm. There are two cases: when the upper part is smaller than the lower part, list the equation: 10 + x2 + 4 = 3x2, the solution is x = 14; when the upper part is larger than the lower part, list the equation: 10 + x2 = 3x2 + 4, the solution is x = 6, then the waist length of the isosceles triangle is 6 or 14cm