1. Ascending and descending order Y3 + Y -2 Y2-1 The expression Y3 + Y - 2 Y2 - 1 can be rearranged in descending and ascending orders as follows:

Descending order: Y3 - 2 Y2 + Y - 1

Ascending order: -1 + Y - 2 Y2 + Y3

2. Ascending and descending order 6-7x5+x4+x3 The expression 6 - 7x5 + x4 + x3 can be rearranged in ascending and descending orders as follows:

Descending order: -7x5 + x4 + x3 + 6

Ascending order: 6 + x3 + x4 - 7x5

3. add up the expressions: 5x3+2x2-1,3x3-7x2+8,x3+2x+1 To add these expressions, we need to first group the like terms:

(5x3 + 3x3 + x3) + (2x2 - 7x2) + (2x + 1) - 1 + 8

Simplifying this, we get:

9x3 - 5x2 + 2x + 8

Therefore, the sum of the expressions 5x3+2x2-1, 3x3-7x2+8, x3+2x+1 is 9x3 - 5x2 + 2x + 8.

4. add up the expressions: xy+x2y2-x3y3,,-xy-x2y2+x3y3,xy+x2y To add these expressions, we group the like terms:

(xy - xy) + (x2y2 - x2y2) + (x3y3 + x3y3) + (xy + xy)

Simplifying this, we get:

2xy + 2x3y3

Therefore, the sum of the expressions xy+x2y2-x3y3, -xy-x2y2+x3y3, xy+x2y is 2xy + 2x3y3.

5. subtract: 7a4+10a5-4a3=9 from 6a5-3a4-7a3+8a-5 To subtract 7a4 + 10a5 - 4a3 + 9 from 6a5 - 3a4 - 7a3 + 8a - 5, we need to change the signs of each term in 7a4 + 10a5 - 4a3 + 9:

-(7a4 + 10a5 - 4a3 + 9)

= -7a4 - 10a5 + 4a3 - 9

Now we can add the like terms:

(6a5 - 10a5) + (-3a4 - 7a4) + (-7a3 + 4a3) + (8a) + (-5 - (-9))

Simplifying this, we get:

-4a5 - 10a4 - 3a3 + 8a + 4

Therefore, the result of subtracting 7a4 + 10a5 - 4a3 + 9 from 6a5 - 3a4 - 7a3 + 8a - 5 is -4a5 - 10a4 - 3a3 + 8a + 4.

6. simplify: [2x+3y-4z]+[3y-6x+5z]+[x-y-z] To simplify the expression [2x+3y-4z]+[3y-6x+5z]+[x-y-z], we can group the like terms:

(2x - 6x + x) + (3y + 3y - y) + (-4z + 5z - z)

Simplifying this, we get:

-3x + 5y

Therefore, [2x+3y-4z]+[3y-6x+5z]+[x-y-z] simplifies to -3x + 5y.

7. if A=2x3-4x2-5, B=4x3-9x-8x2+3 C=-6x2-3x3+2-5x find the value of A+B+C To find the value of A+B+C, we need to add up the expressions for A, B, and C:

A + B + C = (2x^3 - 4x^2 - 5) + (4x^3 - 8x^2 - 9x - 8) + (-3x^3 - 6x^2 - 5x + 2)

Combining like terms, we get:

A + B + C = 2x^3 + 4x^3 - 4x^2 - 8x^2 - 6x^3 - 5x - 8 + 2

Simplifying this, we get:

A + B + C = 0x^3 - 18x^2 - 5x - 6

Therefore, the value of A+B+C is -18x^2 - 5x - 6.

8. Find the product [x+3][x+3] To find the product [x+3][x+3], we can use the distributive property of multiplication over addition:

[x + 3][x + 3] = x[x] + x[3] + 3[x] + 3[3]

Simplifying this, we get:

[x + 3][x + 3] = x^2 + 3x + 3x + 9

Combining like terms, we get:

[x + 3][x + 3] = x^2 + 6x + 9

Therefore, the product of [x+3][x+3] is x^2 + 6x + 9.

9. find the product [y+9][y-9] To find the product [y+9][y-9], we can use the distributive property of multiplication over addition:

[y + 9][y - 9] = y[y] + y[-9] + 9[y] + 9[-9]

Simplifying this, we get:

[y + 9][y - 9] = y^2 - 9y + 9y - 81

Combining like terms, we get:

[y + 9][y - 9] = y^2 - 81

Therefore, the product of [y+9][y-9] is y^2 - 81.

10. find the product : if A=2p-3q-4r and B=-4q+5p-2r,find the value of 3A-4B To find the value of 3A - 4B, we first need to multiply A and B by their respective coefficients:

3A = 3(2p - 3q - 4r) = 6p - 9q - 12r

4B = 4(-4q + 5p - 2r) = -16q + 20p - 8r

Now we can subtract 4B from 3A:

3A - 4B = (6p - 9q - 12r) - (-16q + 20p - 8r)

Simplifying this, we get:

3A - 4B = 6p - 20p - 9q + 16q - 12r + 8r

Combining like terms, we get:

3A - 4B = -14p + 7q - 4r

Therefore, the value of 3A - 4B is -14p + 7q - 4r.

11. evaluate: -3P +2Q-R,when P=-3x3+4x2-1,Q=-7x+2x3-8,R=x3-x2+x-1 Substitute the values of P, Q, and R into the expression -3P + 2Q - R:

-3P + 2Q - R = -3(-3x^3 + 4x^2 - 1) + 2(-7x + 2x^3 - 8) - (x^3 - x^2 + x - 1)

Simplifying this, we get:

-3P + 2Q - R = 9x^3 - 12x^2 + 3 + (-14x + 4x^3 - 16) - x^3 + x^2 - x + 1

Combining like terms, we get:

-3P + 2Q - R = 12x^3 - 11x^2 - 15x - 12

Therefore, when P = -3x^3 + 4x^2 - 1, Q = -7x + 2x^3 - 8, and R = x^3 - x^2 + x - 1, the value of -3P + 2Q - R is 12x^3 - 11x^2 - 15x - 12.

12. divide: x6+4x5-16x3+x+2x2+3-3x4 by x3+4x2+1+2x

We can use polynomial long division to divide x^6 + 4x^5 - 16x^3 + x + 2x^2 + 3 - 3x^4 by x^3 + 4x^2 + 1 + 2x:

x^3 - 2x^2 - 5x + 7 ---------------------------------- x^3 + 4x^2 + 1 + 2x | x^6 + 4x^5 - 16x^3 + x + 2x^2 + 3 - 3x^4 - (x^6 + 4x^5 + x^4 + 2x^4) --------------------------------- - 18x^4 - 16x^3 + 2x^2 - (- 18x^4 - 72x^3 - 18x^2) ---------------------------- 56x^3 + 20x^2 - (56x^3 + 224x^2 + 56x) ----------------------- - 204x^2 + x - (-204x^2 - 816x - 204) ------------------------- 817x + 207

Therefore, the quotient is x^3 - 2x^2 - 5x + 7, and the remainder is 817x + 207. So, we can write:

x^6 + 4x^5 - 16x^3 + x + 2x^2 + 3 - 3x^4 = (x^3 - 2x^2 - 5x + 7)(x^3 + 4x^2 + 1 + 2x) + 817x + 207.

13. for what value of q is the expression 5x3-14x+q exactly divisible by x-2

We can use polynomial long division to find the value of q that makes 5x^3 - 14x + q exactly divisible by x - 2:

5x^2 + 10x + 16 ---------------------------- x - 2 | 5x^3 + 0x^2 - 14x + q - (5x^3 - 10x^2) ------------------- 10x^2 - 14x - (10x^2 - 20x) -------------- 6x - (6x - q) --------- q

For the expression to be exactly divisible by x - 2, the remainder q must be zero. Therefore, we can set the remainder equal to zero:

6x - q = 0

Solving for q, we get:

q = 6x

So, for any value of x, the expression 5x^3 - 14x + 6x is exactly divisible by x - 2