Tạ Quang Tùng
Giới thiệu về bản thân
Ta có
\(P \left(\right. x \left.\right) = x^{4} - 5 x^{3} + 4 x - 5\) \(Q \left(\right. x \left.\right) = - x^{4} + 3 x^{2} + 2 x + 1\)a) Tính \(P \left(\right. x \left.\right) + Q \left(\right. x \left.\right)\)
\(P \left(\right. x \left.\right) + Q \left(\right. x \left.\right) = \left(\right. x^{4} - 5 x^{3} + 4 x - 5 \left.\right) + \left(\right. - x^{4} + 3 x^{2} + 2 x + 1 \left.\right)\) \(= x^{4} - 5 x^{3} + 4 x - 5 - x^{4} + 3 x^{2} + 2 x + 1\)
\(= - 5 x^{3} + 3 x^{2} + 6 x - 4\)
\(P\left(\right.x\left.\right)+Q\left(\right.x\left.\right)=-5x^3+3x^2+6x-4\)
b) Tìm \(R \left(\right. x \left.\right)\) sao cho \(P \left(\right. x \left.\right) = R \left(\right. x \left.\right) + Q \left(\right. x \left.\right)\)
\(R \left(\right. x \left.\right) = P \left(\right. x \left.\right) - Q \left(\right. x \left.\right)\)\(= \left(\right. x^{4} - 5 x^{3} + 4 x - 5 \left.\right) - \left(\right. - x^{4} + 3 x^{2} + 2 x + 1 \left.\right)\)
\(= x^{4} - 5 x^{3} + 4 x - 5 + x^{4} - 3 x^{2} - 2 x - 1\)
\(= 2 x^{4} - 5 x^{3} - 3 x^{2} + 2 x - 6\)
\(R\left(\right.x\left.\right)=2x^4-5x^3-3x^2+2x-6\)
5x(4x2−2x+1)−2x(10x2−5x+2)=−36
=\(5 x \left(\right. 4 x^{2} - 2 x + 1 \left.\right) = 20 x^{3} - 10 x^{2} + 5 x\) \(2 x \left(\right. 10 x^{2} - 5 x + 2 \left.\right) = 20 x^{3} - 10 x^{2} + 4 x\)
=\(\left(\right. 20 x^{3} - 10 x^{2} + 5 x \left.\right) - \left(\right. 20 x^{3} - 10 x^{2} + 4 x \left.\right)\)
=\(20 x^{3} - 10 x^{2} + 5 x - 20 x^{3} + 10 x^{2} - 4 x = x\)
x=-36
5x(4x2−2x+1)−2x(10x2−5x+2)=−36
=\(5 x \left(\right. 4 x^{2} - 2 x + 1 \left.\right) = 20 x^{3} - 10 x^{2} + 5 x\) \(2 x \left(\right. 10 x^{2} - 5 x + 2 \left.\right) = 20 x^{3} - 10 x^{2} + 4 x\)
=\(\left(\right. 20 x^{3} - 10 x^{2} + 5 x \left.\right) - \left(\right. 20 x^{3} - 10 x^{2} + 4 x \left.\right)\)
=\(20 x^{3} - 10 x^{2} + 5 x - 20 x^{3} + 10 x^{2} - 4 x = x\)
x=-36