Question

P(x)=5+x³-2x+4x³+3x²-10

Q(x)=4-5x³+2x²-x³+6x+11x³-8x

a) thu gọn và sắp xếp theo lũy thừa giảm dần của biến

b) tính P(x)+Q(x);P(x)-Q(x)

c) tìm nghiêm đa thức P(x)-Q(x)

Answer 1

a, P(x)= 5+x\(^3\)-2x+4x\(^3\)+3x\(^2\)-10

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

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

sắp xếp : P(x) = -5 - 2x + 3x\(^2\) + 5x\(^3\)

Q(x)=4-5x\(^3\)+2x\(^2\)-x\(^3\)+6x+11x\(^3\)-8x

= 4 - (5x\(^3\)-x\(^3\)+11x\(^3\)) + 2x\(^2\) + (6x - 8x)

= 4 - 15x\(^3\) + 2x\(^2\) - 2x

Sắp xếp : Q(x) = 4 - 2x + 2x\(^2\) -15 x\(^3\)

b, P(x) + Q(x) = ( -5-2x+3x\(^2\)+5x\(^3\)) + (4-2x+2x\(^2\)-15x\(^3\))

= -5 -2x + 3x\(^2\) + 5x\(^3\) + 4 - 2x + 2x\(^2\) - 15x\(^3\)

= (-5 + 4) + (-2x-2x) + (3x\(^2\)+ 2x\(^2\)) + (5x\(^3\) - 15x\(^3\))

=- 1 -4x+ 5x\(^2\) - 10x\(^3\)

P(x) - Q(x) = (-5-2x+3x\(^2\)+5x\(^3\)) - (4-2x+2x\(^2\)-15x\(^3\))

= -5-2x+3x\(^2\)+5x\(^3\)- 4+2x-2x\(^2\)+15x\(^3\)

= (-5-4) + (-2x+2x) + (3x\(^2\)-2x\(^2\)) + (5x\(^3\)+15x\(^3\))

= -9 + x\(^2\) + 20x\(^3\)