Question

dane sa wielomiany

w(X)=4xdo potegi 4-6xdo potegi3+4 P(X)=-2x do potegi 4 +6x do potegi 2 -6

a)P(x)+w(x)

b)w(x)-p(x)

c)p(x)-w(x)

rozwiaz trzy przyklady.

Answer 1

w(x) = 4x^4 -6x^3 + 4

P(x) =-2x^4 + 6x^2 -6

 

a)P(x)+w(x)=

=-2x^4 + 6x^2 -6+ 4x^4 -6x^3 + 4= 2x^4-6x^3+6x^3 -2=2(x^4 -3x^3+3x^2-1)

 

b)

w(x)-p(x)=

=4x^4 -6x^3 + 4 - (-2x^4 + 6x^2 -6) = 4x^4 -6x^3 + 4 + 2x^4 -6x^2 + 6 = 6x^4-6x^3-6x^2+10=

= 2(3x^4-3x^3-3x^2+5)

 

c)p(x)-w(x)=

 =-2x^4 + 6x^2 -6 - (4x^4 -6x^3 + 4)=-2x^4 + 6x^2 -6 -4x^4 + 6x^3 -4 =

 = -6x^4 +6x^3 + 6x^2 -10 = -2(3x^4 -3x^3 -3x^2 +5)

Answer 2

W(x) = 4x⁴-6x³+4

P(x) = -2x⁴+6x²-6

 

a)

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

b)

W(x)-P(x) = 4x⁴-6x³+4-(-2x⁴+6x²-6) = 4x⁴-6x³+4+2x⁴-6x²+6 = 6x⁴-6x³-6x²+10

c)

P(x)-W(x) = -2x⁴+6x²-6-(4x⁴-6x³+4) = -2x⁴+6x²-6-4x⁴+6x³-4 = -6x⁴+6x³+6x²-10