a.P(x)=x7−80x6+80x5−80x4+....+80x+15a.P(x)=x7−80x6+80x5−80x4+....+80x+15

=x7−79x6−x6+79x5+x5−79x4−....−x2+79x+x+15=x7−79x6−x6+79x5+x5−79x4−....−x2+79x+x+15

=x6(x−79)−x5(x−79)+x4(x−79)−....−x(x−79)+x+15=x6(x−79)−x5(x−79)+x4(x−79)−....−x(x−79)+x+15

=(x−79)(x6−x5+x4−....−x)+x+15=(x−79)(x6−x5+x4−....−x)+x+15

Thay x = 79 vào biểu thức trên , ta có

P(79)=(79−79)(796−795+794−...−79)+79+15P(79)=(79−79)(796−795+794−...−79)+79+15

=0+79+15=0+79+15

=94=94

Vậy P(x)=94P(x)=94khi x = 79

b.Q(x)=x14−10x13+10x12−.....+10x2−10x+10b.Q(x)=x14−10x13+10x12−.....+10x2−10x+10

=x14−9x13−x13+9x12+.....−x3+9x2+x2−9x−x+10=x14−9x13−x13+9x12+.....−x3+9x2+x2−9x−x+10

=x13(x−9)−x12(x−9)+.....−x2(x−9)+x(x−9)−x+10=x13(x−9)−x12(x−9)+.....−x2(x−9)+x(x−9)−x+10

=(x−9)(x13−x12+.....−x2+x)−x+10=(x−9)(x13−x12+.....−x2+x)−x+10

Thay x = 9 vào biểu thức trên , ta có

Q(9)=(9−9)(913−912+.....−92+9)−9+10Q(9)=(9−9)(913−912+.....−92+9)−9+10

=0−9+10=0−9+10

=1=1

Vậy Q(x)=1Q(x)=1khi x = 9

c.R(x)=x4−17x3+17x2−17x+20c.R(x)=x4−17x3+17x2−17x+20

=x4−16x3−x3+16x2+x2−16x−x+20=x4−16x3−x3+16x2+x2−16x−x+20

=x3(x−16)−x2(x−16)+x(x−16)−x+20=x3(x−16)−x2(x−16)+x(x−16)−x+20

=(x−16)(x3−x2+x)−x+20=(x−16)(x3−x2+x)−x+20

Thay x = 16 vào biểu thức trên , ta có

R(16)=(16−16)(163−162+16)−16+20R(16)=(16−16)(163−162+16)−16+20

=0−16+20=0−16+20

=4=4

Vậy R(x)=4R(x)=4khi x = 16

d.S(x)=x10−13x9+13x8−13x7+.....+13x2−13x+10d.S(x)=x10−13x9+13x8−13x7+.....+13x2−13x+10

=x10−12x9−x9+12x8+.....+x2−12x−x+10=x10−12x9−x9+12x8+.....+x2−12x−x+10

=x9(x−12)−x8(x−12)+....+x(x−12)−x+10=x9(x−12)−x8(x−12)+....+x(x−12)−x+10

=(x−12)(x9−x8+....+x)−x+10=(x−12)(x9−x8+....+x)−x+10

Thay x = 12 vào biểu thức trên , ta có

S(12)=(12−12)(129−128+....+12)−12+10S(12)=(12−12)(129−128+....+12)−12+10

=0−12+10=0−12+10

=−2=−2

Vậy S(x)=−2S(x)=−2khi x = 12

hok tốt nha

Ta có x=9 => 10=x+1

Thay vào ta có:

Q(x)=x14−(x+1)x13+(x+1)x12−(x+1)x11...−(x+1)x+x+1Q(x)=x14−(x+1)x13+(x+1)x12−(x+1)x11...−(x+1)x+x+1

=x14−x14−x13+x13+x12−x12−x11+...−x2−x+x+1=1=x14−x14−x13+x13+x12−x12−x11+...−x2−x+x+1=1