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
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 ;-)
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
