Toán P(x) = – 2x^2 + 3x^4 + 5x^3 +x^2 – 1/4 x – 2 Q(x) = 3x^4 + x^2 -1/4 – 3x^3 – x^2 a/ Sắp xếp các hạng tử của mỗi đa thức theo luỹ 26/07/2021 By Alice P(x) = – 2x^2 + 3x^4 + 5x^3 +x^2 – 1/4 x – 2 Q(x) = 3x^4 + x^2 -1/4 – 3x^3 – x^2 a/ Sắp xếp các hạng tử của mỗi đa thức theo luỹ thừa giảm dần của biến. b/ Tính P(x) + Q(x) và P(x) – Q(x) c/ Tính : 2 P(x) + 5 Q(x) và 4 P(x) – 3 Q(x) Mn giúp e vs ạ
`a)` `P(x)=- 2x^2 + 3x^4 + 5x^3 +x^2 – 1/4 x – 2 ` `=3x^4+5x^3+(-2x^2+x^2)-1/4x-2` `=3x^4+5x^3-x^2-1/4x-2` “ `Q(x)=3x^4+x^2-1/4-3x^3-x^2` `=3x^4-3x^3+(x^2-x^2)-1/4` `=3x^4-3x^3-1/4` “ `b)` `P(x)+Q(x)` `=(3x^4+5x^3-x^2-1/4x-2)+(3x^4-3x^3-1/4)` `=3x^4+5x^3-x^2-1/4-2+3x^4-3x^3-1/4` `=(3x^4+3x^4)+(5x^3-3x^3)-x^2-1/4x+(-2-1/4)` `=6x^4+2x^3-x^2-1/4x-9/4` “ `P(x)-Q(x)` `=(3x^4+5x^3-x^2-1/4x-2)-(3x^4-3x^3-1/4)` `=3x^4+5x^3-x^2-1/4x-2-3x^4+3x^3+1/4` `=(3x^4-3x^4)+(5x^3+3x^3)-x^2-1/4x+(-2+1/4)` `=8x^3-x^2-1/4x-7/4` “ `c)` `2P(x)+5Q(x)` `=2(3x^4+5x^3-x^2-1/4x-2)+5(3x^4-3x^3-1/4)` `=6x^4+10x^3-2x^2-1/2x-4+15x^4-15x^3-5/4` `=21x^4-5x^3-2x^2-1/2x-21/4` “ `4P(x)-3Q(x)` `=4(3x^4+5x^3-x^2-1/4x-2)-3(3x^4-3x^3-1/4)` `=12x^4+20x^3-4x^2-x-8-9x^4+9x^3+3/4` `=3x^4+29x^3-4x^2-x-29/4` Trả lời
a) $P(x) = 3x^{4} + 5x³ + x² – 2x² – \frac{1}{4}x – 2 = 3x^{4} + 5x³ – x² – \frac{1}{4}x – 2$ $Q(x) = 3x^{4} – 3x³ + x² – x² – \frac{1}{4} = 3x^{4} – 3x³ – \frac{1}{4}$ b) $P(x) + Q(x)$ $= 3x^{4} + 5x³ – x² – \frac{1}{4}x – 2 + 3x^{4} – 3x³ – \frac{1}{4}$ $= (3 + 3)x^{4} + (5 – 3)x³ – x²- \frac{1}{4}x – 2 – \frac{1}{4}$ $= 6x^{4} + 2x³ – x² – \frac{1}{4}x – \frac{9}{4}$ $P(x) – Q(x)$ $= 3x^{4} + 5x³ – x² – \frac{1}{4}x – 2- 3x^{4} + 3x³ + \frac{1}{4}$ $ = (3 – 3)x^{4} + (5 + 3)x³ – x²- \frac{1}{4}x – 2 + \frac{1}{4}$ $= 8x³ – x² – \frac{1}{4}x – \frac{7}{4}$ c) $2P(x) + 5Q(x)$ $= 2(3x^{4} + 5x³ – x² – \frac{1}{4}x – 2) + 5(3x^{4} – 3x³ – \frac{1}{4})$ $= 6x^{4} + 10x³ – 2x² – \frac{1}{2}x – 4 + 15x^{4} – 15x³ – \frac{5}{4}$ $= (6 + 15)x^{4} + (10 – 15)x³ – 2x²- \frac{1}{2}x – 4 – \frac{5}{4}$ $= 21x^{4} – 5x³ – 2x² – \frac{1}{2}x – \frac{21}{4}$ $4P(x) – 3Q(x)$ $= 4(3x^{4} + 5x³ – x² – \frac{1}{4}x – 2) – 3(3x^{4} – 3x³ – \frac{1}{4})$ $= 12x^{4} + 20x³ – 4x² – x – 8 – 9x^{4} + 9x³ + \frac{3}{4}$ $= (12 – 9)x^{4} + (20 + 9)x³ – 4x²- x – 8 + \frac{3}{4}$ $= 3x^{4} + 29x³ – 4x² – x – \frac{29}{4}$ Trả lời