Factorization: x ^ 3 + (a + 17) x ^ 2 + (38-a) x-56

Factorization: x ^ 3 + (a + 17) x ^ 2 + (38-a) x-56

Original formula = x ^ 3-x ^ 2 + (a + 18) x ^ 2 + [56 - (a + 18)] x-56
=x^2(x-1)+(a+18)x^2-(a+18)x+56x-56
=x^2(x-1)+(a+18)x(x-1)+56(x-1)
=(x-1)(x^2+ax+18x+56)

How to decompose (A & sup2; - 7a + 6) (A & sup2; - a-6) + 56 by substitution

Original formula = (A-1) (a-6) (A-3) (a + 2) + 56
=[(a-1)(a-3)][(a-6)(a+2)]+56
=[(a²-4a)+3][(a²-4a)-12]+56
Let x = A & sup2; - 4A
Original formula = (x + 3) (X-12) + 56
=x²-9x-36+56
=x²-9x+20
=(x-4)(x-5)
=(a²-4a-4)(a²-4a-5)
=(a²-4a-4)(a-5)(a+1)

Given that the symmetry axis of the image of the square of the function y = a (x + b) is a straight line x = 1 and intersects with the Y axis at the point P (0.3), the values of a and D are obtained

Because the symmetry axis of y = a (x + b) ^ 2 is x = - B = 1, that is, B = - 1
When x = 0, y = 3, that is, 3 = a (0-1) ^ 2, the solution is a = 3
^This is the square
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Simplify evaluation: find the value of (4a2-5ab + B2) - (2a2-3ab + 3B2), where A2-B2 = 5, ab = 2

The original formula is 4a2-5ab + b2-2a2 + 3ab-3b2 = 2a2-2b2-2ab = 2 (A2-B2) - 2Ab. When A2-B2 = 5 and ab = 2, the original formula is 10-4 = 6

ABCD is a parallelogram. Circle O with diameter AB intersects diagonal BD at point P, intersects edge BC at point Q, connects AQ, intersects BD at point E. BP = PD is known
If AE = 4, EQ = 2, find the area of ABCD

P is the midpoint of BD, P is also the midpoint of AC, and on the circle, ∠ APB = 90  quadrilateral ABCD is a diamond
Δ ape ∽ AQC AP / AQ = AE / AC ∽ AP = 2 radical 3 AC = 2AP = 4 radical 3
Using Pythagorean theorem, we can get QC = 2 radical, 3 ∠ ACB = 60 degree
Ψ BC = AC = 4 radical 3
Area of quadrilateral ABCD = AQ * BC = 6 * 4 root sign 3 = 24 root sign 3

The area of a trapezoid is 36 square centimeters, the bottom is 7 centimeters, the height is 4 centimeters, and the upper bottom is () centimeters long

11

In triangle ABC, angle a > angle c, and the degree of angle a, angle B and angle c satisfies the formula (angle a + angle c) (angle a-angle C) = (square of angle b)
Request the degree of angle A and angle C

There is no definite solution to this problem
Because Party A = Party B + Party C
You can find any group of Pythagorean numbers and multiply them by a coefficient to ensure that the sum is 180
For example, you look for 3, 4, 5 and multiply by 15
So 45 60 75 meets the conditions

What's the idiom "stars, sun and mountains"

Few as morning stars
Sparse: sparse. As rare as the stars in the morning
[from]: in the Southern Dynasty, Qi Xie Tiao's "night hair on the road to Beijing" said: "the morning light is falling, and the morning light is reflected again." in Tang Han Yu's "Huashan girl" poem: "Taoist priest Huang Yi also said that there are few stars under his seat."
Example: neishan Bookstore often goes to the bookstore, but not every day
Lu Xun's collection of letters
Grammar: more formal; used as predicate or attribute; used of people or things

Who will?

1.×
2.×
3.√

A rectangular pool, the scale is 1:2000. Find the actual floor area of the rectangular pool. The length of the rectangle is 3.5cm, the width is 1.5cm

The actual length is 3.5 * 2000 = 7000cm = 70m
Width 1.5 * 2000 = 3000cm = 30m
Area = 70 * 30 = 2100 square meters