bạn tham khảo nha

a, P(x) = 5x⁴+3x-4x³-7x²+1

+ Q(x) =5x⁴-4x³-6x²+3x-8

P(x) + Q(x) =10x⁴-8x³-13x²+6x-7

P(x) - Q(x) =-x²+9

Để P(x) =Q(x) 

=> P(x) -Q(x) =-x²+9 =0

                  => -x² = 9

=> x=3

K MK NHA. CHÚC BẠN HỌC GIỎI

a: \(P\left(x\right)=x^5+2x^4-9x^3-x\)

\(Q\left(x\right)=5x^4+9x^3+4x^2-14\)

c:: \(M\left(x\right)=P\left(x\right)+Q\left(x\right)=x^5+7x^4+4x^2-x-14\)

d: \(M\left(2\right)=32+7\cdot16+4\cdot4-2-14=144\)

\(M\left(-2\right)=-32+7\cdot16+4\cdot4+2-14=84\)

P(x) + Q(x)= ( x^5 - 2x^2 + 7x^4 - 9x^3 - 1/4x) + ( 5x^4 - x^5 + 4x^2 - 2x^3 - 1/4)

                 = x^5 - 2x^2 + 7x^4 - 9x^3 - 1/4x + 5x^4 - x^5 + 4x^2 - 2x^3 - 1/4

                 = ( x^5 - x^5 ) - ( 2x^2 + 4x^2) + ( 7x^4 + 5x^4) - ( 9x^3 - 2x^3) - 1/4x - 1/4

                 =                            6x^2 + 12x^4 - 6x^3 - 1/4x - 1/4

P(x) - Q(x)=  ( x^5 - 2x^2 + 7x^4 - 9x^3 -1/4x) - ( 5x^4 - x^5 + 4x^2 - 2x^3 -1/4)

                 = x^5 - 2x^2 + 7x^4 - 9x^3 - 1/4x - 5x^4 + x^5 - 4x^2 + 2x^3 + 1/4

                 = ( x^5 + x^5) - ( 2x^2 - 4x^2) + ( 7x^4 - 5x^4) - ( 9x^3 + 2x^3) - 1/4x + 1/4

                 = 2x^5 - (-2)x^2 + 2x^4 - 11x^3 - 1/4x + 1/4

P(x)=x^5+  7x^4- 9x^3+ 2x^2-1/4x-0

Q(x)=(-x^5+5x^4- 2x^3+ 4x^2+0x-1/4

      =      12x^4-11x^3+ 6x^2-1/4x-1/4

a) Thu gọn, sắp xếp các đa thức theo lũy thừa tăng của biến

$f\left(x\right)=x^2+2x^3-7x^5-9-6x^7+x^3+x^2+x^5-4x^2+3x^7$

= -9 - 2x² + 3x³ - 6x⁵ - 3x⁷

$g\left(x\right)=x^5+2x^3-5x^8-x^7+x^3+4x^2-5x^7+x^4-4x^2-x^6-12$

$\mathrm{=\; -12\; +\; 3x3\; +\; x4\; +\; x5\; -\; x6\; -\; 6x7\; -\; 5x8}$

$h\left(x\right)=x+4x^5-5x^6-x^7+4x^3+x^2-2x^7+x^6-4x^2-7x^7+x$

$\mathrm{=\; 2x\; -\; 3x2\; +\; 4x3\; +4x5\; -4x6\; -\; 10x7}$

b) Tính $f\left(x\right)+g\left(x\right)-h(x)\; =\; ($-9 - 2x² + 3x³ - 6x⁵ - 3x⁷ ) + (-12 + 3x³ + x⁴ + x⁵ - x⁶ - 6x⁷ - 5x⁸ ) - (2x - 3x² + 4x³ +4x⁵ -4x⁶ - 10x⁷)

= - 9 - 2x² + 3x³ - 6x⁵ - 3x⁷ -12 + 3x³ + x⁴ + x⁵ - x⁶ - 6x⁷ - 5x⁸ - 2x + 3x² - 4x³ - 4x⁵ + 4x⁶ + 10x⁷

= -21 - 2x + x² + 2x³ + x⁴ - 9x⁵ + 3x⁶ + x⁷ - 5x⁸

a: \(P\left(x\right)+Q\left(x\right)=9x^3-6x^2+x-3\)

\(P\left(x\right)-Q\left(x\right)=-x^3-6x^2+13x-7\)

b: \(P\left(1\right)=4-6+7-5=-2+7-5=0\)

\(P\left(-2\right)=-32-24-14-5=-73\)

P(x) = x^5 - 2x^2 + 7x^4 - 9x^3 - 1/4x

=x⁵+7x⁴-9x³-2x²-1/4x

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

=-x⁵+5x⁴-2x³+4x²-1/4

P(x)+Q(x)=x⁵+7x⁴-9x³-2x²-1/4x -x⁵+5x⁴-2x³+4x²-1/4

=x⁵-x⁵+7x⁴+5x⁴-9x³-2x³-2x²+4x²-1/4x-1/4

=12x⁴-11x³+2x²-1/4x-1/4

P(x)-Q(x)=x⁵+7x⁴-9x³-2x²-1/4x +x⁵-5x⁴+2x³-4x²+1/4

=x⁵+x⁵+7x⁴-5x⁴-9x³+2x³-2x²-4x²-1/4x-1/4

=2x⁵+2x⁴-7x³-6x²-1/4x-1/4