Bài 3. Cho đa thức sau
P(x)= -2x\(^4\) - 7x +\(\dfrac{1}{2}\) - 6x\(^4\) + 2x\(^2\) - x
Q(x)= 3x\(^3\) - x\(^4\) - 5x\(^2\) + x\(^3\) - 6x + \(\dfrac{3}{4}\)
a) Thu gọn các đa thức trên
b) Tính P(x) + Q(x), P(x) - Q(x)
Bài 4. Cho 3 đa thức
P(x)= 3x - 2x\(^2\) - 2 + 6x\(^3\)
Q(x)= 3x\(^2\) - x - 2x\(^3\) + 4
R(x)= 1 + 4x\(^3\) - 2x
Tính P(x) + Q(x) - R(x), R(x) - P(x) - Q(x).
Giúp mình trước 8h với
Bài 4:
P(x)+Q(x)-R(x)
\(=6x^3-2x^2+3x-2-2x^3+3x^2-x+4-4x^3+2x-1\)
\(=x^2+4x+1\)
R(x)-P(x)-Q(x)
\(=-\left[P\left(x\right)+Q\left(x\right)-R\left(x\right)\right]\)
\(=-\left(x^2+4x+1\right)\)
\(=-x^2-4x-1\)
Bài 3:
a: \(P\left(x\right)=-2x^4-7x+\dfrac{1}{2}-6x^4+2x^2-x\)
\(=\left(-2x^4-6x^4\right)+2x^2+\left(-7x-x\right)+\dfrac{1}{2}\)
\(=-8x^4+2x^2-8x+\dfrac{1}{2}\)
\(Q\left(x\right)=3x^3-x^4-5x^2+x^3-6x+\dfrac{3}{4}\)
\(=-x^4+\left(3x^3+x^3\right)+\left(-5x^2\right)-6x+\dfrac{3}{4}\)
\(=-x^4+4x^3-5x^2-6x+\dfrac{3}{4}\)
b: P(x)+Q(x)
\(=-8x^4+2x^2-8x+\dfrac{1}{2}-x^4+4x^3-5x^2-6x+\dfrac{3}{4}\)
\(=-9x^4+4x^3-3x^2-14x+\dfrac{5}{4}\)
P(x)-Q(x)
\(=-8x^4+2x^2-8x+\dfrac{1}{2}+x^4-4x^3+5x^2+6x-\dfrac{3}{4}\)
\(=-7x^4-4x^3+7x^2-2x-\dfrac{1}{4}\)