2x4:x2=2x2

2x2(x2−2)=2x4−4x2

(2x4−3x3−3x2+6x−2)−(2x4−4x2)

−3x3+x2+6x−2

−3x3:x2=−3x

−3x(x2−2)=−3x3+6x

(−3x3+x2+6x−2)−(−3x3+6x)

x2−2

x2:x2=1

1(x2−2)=x2−2

(x2−2)−(x2−2)=0

Thương =2x2−3x+1​

Dư = 0\(\)

2x4:x2=2x2

2x2(x2−2)=2x4−4x2

(2x4−3x3−3x2+6x−2)−(2x4−4x2)

−3x3+x2+6x−2

−3x3:x2=−3x

−3x(x2−2)=−3x3+6x

(−3x3+x2+6x−2)−(−3x3+6x)

x2−2

x2:x2=1

1(x2−2)=x2−2

(x2−2)−(x2−2)=0

Thương =2x2−3x+1​

Dư = 0\(\)

5x(4x2−2x+1)=20x3−10x2+5x

2x(10x2−5x+2)=20x3−10x2+4x

20x3−10x2+5x−(20x3−10x2+4x)=−36

20x3−10x2+5x−20x3+10x2−4x=−36

(20x3−20x3)+(−10x2+10x2)+(5x−4x)=−36 \(x = - 36\)

vậy x=−36

Ta có:

\(P \left(\right. x \left.\right) + Q \left(\right. x \left.\right) = \left(\right. x^{4} - 5 x^{3} + 4 x - 5 \left.\right) + \left(\right. - x^{4} + 3 x^{2} + 2 x + 1 \left.\right)\)

=(x4−x4)+(−5x3)+(3x2)+(4x+2x)+(−5+1)

=0−5x3+3x2+6x−4

Vậy: P(x)+Q(x)=−5x3+3x2+6x−4​

Ta có:

\(R \left(\right. x \left.\right) = P \left(\right. x \left.\right) - Q \left(\right. x \left.\right)\) \(R \left(\right. x \left.\right) = \left(\right. x^{4} - 5 x^{3} + 4 x - 5 \left.\right) - \left(\right. - x^{4} + 3 x^{2} + 2 x + 1 \left.\right)\)

R(x)=x4−5x3+4x−5+x4−3x2−2x−1

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

\(= 2 x^{4} - 5 x^{3} - 3 x^{2} + 2 x - 6\)

\(R\left(\right.x\left.\right)=2x^4-5x^3-3x^2+2x-6\)\(\)