Bài 5

a) \(A\left(x\right)=5x^4-2x^3+x^2-4\)

\(B\left(x\right)=-x^5+7x^4-3x^2-9x^3+7\)

\(=-x^5+7x^4-9x^3-3x^2+7\)

b) \(2C\left(x\right)+A\left(x\right)=3C\left(x\right)-B\left(x\right)\)

\(\Rightarrow3C\left(x\right)-2C\left(x\right)=A\left(x\right)+B\left(x\right)\)

\(\Rightarrow C\left(x\right)=A\left(x\right)+B\left(x\right)\)

\(=\left(5x^4-2x^3+x^2-4\right)+\left(-x^5+7x^4-9x^3-3x^2+7\right)\)

\(=5x^4-2x^3+x^2-4-x^5+7x^4-9x^3-3x^2+7\)

\(=-x^5+\left(5x^4+7x^4\right)+\left(-2x^3-9x^3\right)+\left(x^2-3x^2\right)+\left(-4+7\right)\)

\(=-x^5+12x^4-11x^3-2x^2+3\)

c) C(x) có:

- Hệ số cao nhất: -1

- Hệ số lũy thừa bậc 2: -2

- Hệ số tự do: 3

- Bậc: 5

Bài 4:

a) \(P=3x-2x^2-2x+6x^3\)

\(=\left(3x-2x\right)-2x^2+6x^3\)

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

\(Q=x^2-x-2x^3+4\)

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

b) \(R=P+Q\)

\(=\left(x-2x^2+6x^3\right)+\left(4-x+x^2-2x^3\right)\)

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

\(=\left(6x^3-2x^3\right)+\left(-2x^2+x^2\right)+\left(x-x\right)+4\)

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

----------------------------------------------------------

\(H=P-Q\)

\(=\left(x-2x^2+6x^3\right)-\left(4-x+x^2-2x^3\right)\)

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

\(\left(6x^3+2x^3\right)+\left(-2x^2-x^2\right)+\left(x+x\right)-4\)

\(=8x^3-3x^2+2x-4\)

---------------------------------------------------

e) \(R\left(4\right)=4.4^3-4^2+4\)

\(=256-16+4\)

\(=244\)

\(H\left(-5\right)=8.\left(-5\right)^3-3.\left(-5\right)^2+2.\left(-5\right)-4\)

\(=-1000-75-10-4\)

\(=-1089\)

Bài 3

a) \(A=3x^2+x+x^4-x^3-x^2+2x\)

\(=x^4-x^3+\left(3x^2-x^2\right)+\left(x+2x\right)\)

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

\(B=x^4+2x^2+x^3\)

\(=x^4+x^3+2x^2\)

b) * Đa thức A có:

- Bậc: 4

- Hệ số tự do: 0

- Hệ số cao nhất: 1

* Đa thức B có:

- Bậc: 4

- Hệ số tự do: 0

- Hệ số cao nhất: 1

c) \(A+B=\left(x^4-x^3+2x^2+3x\right)+\left(x^4+x^3+2x^2\right)\)

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

\(=\left(x^4+x^4\right)+\left(-x^3+x^3\right)+\left(2x^2+2x^2\right)+3x\)

\(=2x^4+4x^2+3x\)

\(A-B=\left(x^4-x^3+2x^2+3x\right)-\left(x^4+x^3+2x^2\right)\)

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

\(=\left(x^4-x^4\right)+\left(-x^3-x^3\right)+\left(2x^2-2x^2\right)+3x\)

\(=-2x^3+3x\)

\(B-A=\left(x^4+x^3+2x^2\right)-\left(x^4-x^3+2x^2+3x\right)\)

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

\(=\left(x^4-x^4\right)+\left(x^3+x^3\right)+\left(2x^2-2x^2\right)-3x\)

\(=2x^3-3x\)

Bài 2

* \(P+Q=\left(x^5+7x^3+1\right)+\left(x^3-4x^5+2\right)\)

\(=x^5+7x^3+1+x^3-4x^5+2\)

\(=\left(x^5-4x^5\right)+\left(7x^3+x^3\right)+\left(1+2\right)\)

\(=-3x^5+8x^3+3\)

* \(P-Q=\left(x^5+7x^3+1\right)-\left(x^3-4x^5+2\right)\)

\(=x^5+7x^3+1-x^3+4x^5-2\)

\(=\left(x^5+4x^5\right)+\left(7x^3-x^3\right)+\left(1-2\right)\)

\(=5x^5+6x^3-1\)

Bài 1:

a) \(A\left(x\right)+B\left(x\right)=\left(-x^3+x^2-5x+1\right)+\left(x^3+4x-5\right)\)

\(=-x^3+x^2-5x+1+x^3+4x-5\)

\(=\left(-x^3+x^3\right)+x^2+\left(-5x+4x\right)+\left(1-5\right)\)

\(=x^2-x-4\)

b) \(A\left(x\right)-B\left(x\right)=\left(-x^3+x^2-5x+1\right)-\left(x^3+4x-5\right)\)

\(=-x^3+x^2-5x+1-x^3-4x+5\)

\(=\left(-x^3-x^3\right)+x^2+\left(-5x-4x\right)+\left(1+5\right)\)

\(=-2x^3+x^2-9x+6\)

var a:array[1..200] of integer;

x,y,i,n:integer;

begin

write('n = ');readln(n);

write('x = ');readln(x);

write('y = ');readln(y);

for i:=1 to n do

begin

write('a[',i,' = ');readln(a[i]);

end;

for i:=1 to n do

if a[i] = x then a[i]:=y;

writeln('Mang sau khi thay the ');

for i:=1 to n do write(a[i]:10);

readln;

end.

var tam,a,b,i:integer;

begin

write('a = ');readln(a);

write('b = ');readln(b);

if a < b then

begin

tam:=a;

a:=b;

b:=tam;

end;

for i:=a to b do

if sqrt(i) = trunc(sqrt(i)) then write(i:10);

readln;

End.

var a:string;

var a:array[1..200] of integer;

min,i,n:integer;

s:longint;

begin

write('Nhap so phan tu n = ');readln(n);

for i:=1 to n do

begin

write('nhap phan tu thu ',i,' = ');readln(a[i]);

end;

writeln('Cac so vua nhap la :');

for i:=1 to n do write(a[i]:10);

writeln('Tong cac phan tu la so le la ');

for i:=1 to n do

if a[i] mod 2 <> 0 then s:=s+a[i];

writeln(s);

writeln('GTNN cua mang la ');

min:=a[1];

for i:=2 to n do

if a[i] < min then min:=a[i];

write(min);

readln;

end.

var i,n:integer;

begin

write('n = ');readln(n);

i:=2;

while n mod i <> 0 do i:=i+1;

if i = n then write(n,' la so nguyen to')

else write(n,' khong la so nguyen to');

readln

end.