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`
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)
$2P(x) + 5Q(x)$
$= 2(3x^{4} + 5x³ – x² – \frac{1}{4}x – 2) + 5(3x^{4} – 3x³ – \frac{1}{4})$
$= 6x^{4} + 10x³ – 2x² – \frac{1}{2}x – 4 + 15x^{4} – 15x³ – \frac{5}{4}$
$= (6 + 15)x^{4} + (10 – 15)x³ – 2x²- \frac{1}{2}x – 4 – \frac{5}{4}$
$= 21x^{4} – 5x³ – 2x² – \frac{1}{2}x – \frac{21}{4}$
$4P(x) – 3Q(x)$
$= 4(3x^{4} + 5x³ – x² – \frac{1}{4}x – 2) – 3(3x^{4} – 3x³ – \frac{1}{4})$
$= 12x^{4} + 20x³ – 4x² – x – 8 – 9x^{4} + 9x³ + \frac{3}{4}$
$= (12 – 9)x^{4} + (20 + 9)x³ – 4x²- x – 8 + \frac{3}{4}$
$= 3x^{4} + 29x³ – 4x² – x – \frac{29}{4}$