[BIL. 4ºESO] Polynomials

A

100

P(x) = 8x³-5x+6x²yz

What is the degree of the polynomial?

4

200

P(x) = 4x³ +6x² -2x+3 

Q(x) = 2x³ -x+7 

R(x) = 7x² -2x+1 

P(x) - Q(x) - R(x) ?

2x³-x²+x-5

300

(3x³-2x²+5)(4x²+3x-1)

12x⁵+x⁴-9x³+22x²+15x-5

400

(-x⁶ +x⁵ -2x³ +7) (x² -x+1)

-x⁸ +2x⁷ -2x⁶ -x⁵ +2x⁴ -2x³ +7x² -7x+7

500

P(x)=4x³ +6x² -2x+3

Q(x)=2x³ -x+7 

R(x)=7x² -2x+1

 P(x)·Q(x)·R(x) ?

 

56x⁸ +68x⁷ -72x⁶ +224x⁵ +244x⁴ -179x³ +225x² -59x+21

B

100

P(x) = -x²-x-2. Calculate the numerical value if x=-2

P(2) = -4

200

P(x)=2x⁵ -3x⁴ +3x² -5 

Q(x)=x⁵ +6x⁴ -4x³ -x+7

P(x)+Q(x)?

3x⁵+3x⁴-4x³+3x²-x+2

300

Extract common factor

P(x) = 4x²-6x+2x³

P(x) = 2x(x²+2x-3)

400

P(x)=4x³ +6x² -2x+3

Q(x)=2x³ -x+7 

R(x)=7x² -2x+1

 P(x)-Q(x)·R(x)?

-14x⁵ +4x⁴ +9x³ -45x² +13x-4

500

2x(5y+2x+1) - x(x-5y) + 7xy

22xy+3x²+2x

C

100

P(x) = x³+2x²-5. Calculate the numerical value if x=-3

P(-3) = -14

200

P(x) = 4x³ +6x² -2x+3 

Q(x) = 2x³ -x+7 

R(x) = 7x² -2x+1 

P(x) + Q(x) + R(x) ?

6x³ +13x² -5x+11

300

P(x) = 4x³ +6x² -2x+3 

Q(x) = 2x³ -x+7 

R(x) = 7x² -2x+1 

P(x) + 3Q(x) - 2R(x) ?

10x³-8x²-x+22

400

P(x)=x²–kx+2. Calculate the value of k if P(-2)=8

k=1

500

(x+1)(2x-5)+5(x²+6x)

7x²+27x-5

D

100

P(x) = 12xy³⁺4zx - 9xy³ + 2xy² + 4 - 3xy³

What is the degree of the polynomial?

3

200

5x³· 3x²y · (−4xz³)=

-60x⁶yz³

300

(x³-2x²+x)(x²+3x-5)

x⁵+x⁴-10x³+13x²-5x

400

P(x)=4x³ +6x² -2x+3

Q(x)=2x³ -x+7 

R(x)=7x² -2x+1

 P(x)·[Q(x)+R(x)] ?

8x⁶ +40x⁵ +26x⁴ +6x³ +75x² -25x+24

500

(3x+2)(x-3)+2x(x-4)+5(x²-6x+3)

10x²-45x+9

E

100

P(x) = –x³–3x²–x+2. Calculate the numerical value if x=-4

P(-4) = -106

200

P(x)=2x⁵ -3x⁴ +3x² -5 

Q(x)=x⁵ +6x⁴ -4x³ -x+7

P(x)-Q(x)?

x⁵-9x⁴+4x³+3x²+x-12

300

Extract common factor

P(x) = 6x³y²-3x²yz+9xy³z² =

3xy(2x²y - xz + 3y²z²)

400

(5x³ -4x² +x-2) (x³ -7x² +3)

5x⁶ -39x⁵ +29x⁴ +6x³ +2x² +3x-6

500

(3a+7b)(a-b)+6a(a-5b+8)+ab-a²

8a²-7b²-25ab+48a