Question

zad 7 , 8 , 9 , 10 w załączniku , po kilka przykładów . daje naj !

Answer 1

zad.7

 

a)

W(x)+Q(x) = (x4+3x3-5x2+x-6)+(x5-4x4+6x3-x2+2x-3) = x4+3x3-5x2+x-6+ x5-4x4+6x3-x2+2x-3 = x5-3x4+9x3-6x2+3x-9

 

b)

W(x)+2P(x) = (x4+3x3-5x2+x-6)+2(2x3+4x2-11x+2) = x4+3x3-5x2+x-6+4x3+8x2-22x+4 =

x4+7x3+3x2-21x-2

 

c)

P(x)+Q(x)+W(x) = (2x3+4x2-11x+2)+(x5-4x4+6x3-x2+2x-3)+(x4+3x3-5x2+x-6) =

= 2x3+4x2-11x+2+ x5-4x4+6x3-x2+2x-3+ x4+3x3-5x2+x-6=

x5-3x4+11x3-2x2-8x-7

 

d)

W(x)-P(x) = (x4+3x3-5x2+x-6)-( 2x3+4x2-11x+2) = x4+3x3-5x2+x-6- 2x3-4x2+11x-2=

x4+x3-9x2+12x-8

 

e)

3Q(x)-W(x) = 3(x5-4x4+6x3-x2+2x-3)-(x4+3x3-5x2+x-6) = 3x5-12x4+18x3-3x2+6x-9-x4-3x3+5x2-x+6 3x5-13x4+15x3+2x2+5x-3

 

f)

[W(x)+P(x)]-Q(x) = [(x4+3x3-5x2+x-6)+( 2x3+4x2-11x+2)]-(x5-4x4+6x3-x2+2x-3) =

= [ x4+3x3-5x2+x-6+ 2x3+4x2-11x+2]- x5+4x4-6x3+x2-2x+3=

= x4+5x3-x2-10x-4- x5+4x4-6x3+x2-2x+3=

-x5+5x4-x3-12x-1

 

 

zad.9

 

a)

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

x3-x2-5x-3+3x3+7x2+x-2 = 4x3+6x2-4x-5

 

b)

(2x2+x)2-(3x2+1)2 = (4x4+4x3+x2)-(9x4+6x2+1)=4x4+4x3+x2-9x4-6x2-1 = -5x4+4x3-5x2+1

 

c)

5(x3+x2+2x+1)(3x-2)-(2x2+3x)2 = 5(3x4+3x3+6x2+3x-2x3-2x2-4x-2)-(4x4+12x3+9x2) =

5(3x4+x3+4x2-x-2)-4x4-12x3-9x2 = 15x4+5x3+20x2-5x-10-4x4-12x3-9x2 =

11x4-7x3+11x2-5x-10

 

d)

-4(x+1)3-(4x+2)(4x-2)+(3x+1)(x2+3x-2) = -4(x3+3x2+3x+1)-(16x2-4)+(3x3+9x2-6x+x2+3x-2) =

-4x3-12x2-12x-4-16x2+4+3x3+10x2-3x-2 = -x3-18x2-15x-2

 

 

Zad.8

 

a)

W(x)-2P(x)+3Q(x) = (4x3-2x2+x-2)-2(x3+3x+1)+3(2x4+x3-x+6) =

= 4x3-2x2+x-2-2x3-6x-2+6x4+3x3-3x+18 =

6x4+5x3-2x2-8x+14

 

b)

Q(x)-[W(x)+P(x)] = (2x4+x3-x+6)-[(4x3-2x2+x-2)+(x3+3x+1)]=

= 2x4+x3-x+6-[ 4x3-2x2+x-2+ x3+3x+1] =

= 2x4+x3-x+6-[5x3-2x2+4x-1] =

= 2x4+x3-x+6- 5x3+2x2-4x+1 =

2x4-4x3+2x2-5x+7

 

c)

W(x)*P(x)-Q(x) = (4x3-2x2+x-2)(x3+3x+1)-(2x4+x3-x+6) =

= 4x6+12x4+4x3-2x5-6x3-2x2+x4+3x2+x-2x3-6x-2-2x4-x3+x-6 =

4x6-2x5+11x4-5x3+x2-4x-8

 

d)

Q(x)-2W(x)-P(x) = (2x4+x3-x+6)-2(4x3-2x2+x-2)-(x3+3x+1) =

= 2x4+x3-x+6-8x3+4x2-2x+4- x3-3x-1 =

2x4-8x3+4x2-6x+5

 

e)

P(x)*[W(x)-Q(x)] = (x3+3x+1)*[(4x3-2x2+x-2)-(2x4+x3-x+6)] =

= (x3+3x+1)*[4x3-2x2+x-2-2x4-x3+x-6] =

= (x3+3x+1)*[-2x4+3x3-2x2+2x-8]=

= 2x7+3x6-2x5+2x4-8x3-6x5+9x4-6x3+6x2-24x-2x4+3x3-2x2+2x-8 =

2x7+3x6-8x5+9x4-11x3-4x2-22x-8

 

f)

[P(x)]2-Q(x)-W(x) = (x3+3x+1)2-(2x4+x3-x+6)-(4x3-2x2+x-2) =

= (x5+9x2+1+6x4+2x3+6x)- 2x4-x3+x-6-4x3+2x2-x+2 =

= x5+6x4+2x3+9x2+6x+1-2x4-5x3+2x2-4 =

x5-4x4-3x3+11x2+6x-3