a
f(-1)=5(-1)³-7(-1)²+(-1)+7=6
g($\frac{-1}{2}$) =7($\frac{-1}{2}$)³-7($\frac{-1}{2}$)²+2($\frac{-1}{2}$)+5
=7)($\frac{-1}{8}$)-7($\frac{1}{2}$)+2($\frac{-1}{2}$)+5
=-0,375
h(0)=2.0²+4.0+1=1
b
A(x)=f(x)-g(x)-h(x)
=(5x³-7x²+x+7)-(7x³-7x²+2x+5)-(2x³+4x+1)
=5x³-7x²+x+7-7x³+7x²-2x-5-2x³-4x-1
=(5x³-7x³-2x³)+(-7x²+7x²)+(x-2x-4x)+(7-5-1)
=-4x³-7x+1
c
B(x)=f(x)-g(x)+h(x)
=(5x³-7x²+x+7)-(7x³-7x²+2x+5)+(2x³+4x+1)
=5x³-7x²+x+7-7x³+7x²-2x-5+2x³+4x+1
=(5x³-7x³+2x³)+(-7x²+7x²)+(x-2x+4x)+(7-5+1)
=4x³+3x+3
d bậc của B(x) là 3
B(x)= 0 ⇒ 4x³+3x+3=0
4x³+3x = -3
mà 4x³+3x>0
⇒đa thức B(x) vô nghiệm)
