Question

Dane są wielomiany u(x) = 2x⁴ + x² - 1 i v(x) = x⁴ - 2x² + 2
Wyznacz wielomian w


a) w(x)= 2u(x) + v(x)

b) w(x)= 2u(x) - 4v(x)

c) w(x)= 3u(x) -½v(x)

d) w(x)= ½u(x) + ¾v(x)

Answer 1

Dane są wielomiany u(x) = 2x⁴ + x² - 1 i v(x) = x⁴ - 2x² + 2
Wyznacz wielomian w


a) w(x)= 2u(x) + v(x)

b) w(x)= 2u(x) - 4v(x)

c) w(x)= 3u(x) -½v(x)

d) w(x)= ½u(x) + ¾v(x)


a) w(x)=2( 2x⁴ + x² - 1)+x⁴ - 2x² + 2
w(x)=4x⁴ +2x²-2 +x⁴ - 2x² + 2=5x⁴

b)w(x)=4x⁴ +2x²-2 - 4(x⁴ - 2x²+ 2)
w(x)=4x⁴ +2x²-2-4x⁴+8x²-8=10x²-10

c)w(x) = 3(2x⁴ + x² - 1) - 1/2(x⁴ - 2x²+ 2)
w(x)=6x⁴+3x²-3 -½x⁴+x²-1
w(x)=5,5⁴+4x²-4

d)½( 2x⁴ + x² - 1) +¾(x⁴ - 2x²+ 2)=
x⁴+½x²-½+¾x⁴ -1,5x²+1,5 =
1 ¾x⁴ - x²+1

Answer 2

U(x) = 2x⁴ + x² - 1 i v(x) = x⁴ - 2x² + 2
a) w(x)= 2u(x) + v(x)
2(2x⁴ + x² - 1)+x⁴ - 2x² + 2=w(x)
4x⁴+2x²-2+x⁴ - 2x² + 2=w(x)
5x⁴=w(x)

b) w(x)= 2u(x) - 4v(x)
2(2x⁴ + x² - 1)-4(x⁴ - 2x² + 2)=w(x)
4x⁴+2x²-2-4x⁴ +8x²-8=w(x)
10x²-10=w(x)
10(x²-1)=w(x)
w(x)=10(x-1)(x+1)

c) w(x)= 3u(x) -½v(x)
3(2x⁴ + x² - 1)-½(x⁴ - 2x² + 2)=
=6x⁴+3x²-3-½x⁴+x²-1=5½x⁴+4x²-4

d) w(x)= ½u(x) + ¾v(x)
½(2x⁴ + x² - 1)+¾(x⁴ - 2x² + 2)=
x⁴+½x²-½+¾x⁴-3/2x²+3/2=¾x⁴-x²+1

proszę ;-)

Answer 3

U(x) = 2x⁴ + x² - 1 i v(x) = x⁴ - 2x² + 2
a) w(x)= 2u(x) + v(x)=2(2x⁴ + x² - 1) + x⁴ - 2x² + 2=
=4x⁴ + 2x² - 2+ x⁴ - 2x² + 2=5x⁴
b) w(x)= 2u(x) - 4v(x)=2(2x⁴ + x² - 1) -4( x⁴ - 2x² + 2)=
=4x⁴ + 2x² - 2-4x⁴ + 8x²-8=10x²-10
c) w(x)= 3u(x) -½v(x)=3(2x⁴ + x² - 1)- ½( x⁴ - 2x² + 2)=
=6x⁴ + 3x² -3- ½ x⁴+x²-1=5½ x⁴+4x²-4
d) w(x)= ½u(x) + ¾v(x)=½(2x⁴ + x² - 1)+ ¾( x⁴ - 2x² + 2)=
=x⁴ +½x² -½+¾x⁴-1½x²+1½=1¾x⁴-x²+1