Polynomials Review

Adding

100

(4a² + 1) + (2a² + 9)

6a² +10

200

(3a² + 4a - 2) + (6a³ -2a + 7)

6a³ + 3a² + 2a +5

300

(7a + 3 - 2a²) + (3a² - 4a + 1)

a² + 3a + 4

400

(5b⁵ + 8b³ - 7b² - 10) + (-3b⁵ - 4b⁴ + 6b³ + 17)

2b⁵ - 4b⁴ + 14b³ + 7

500

(5m⁴ - 7m³ + m - 4) + ( 3m³ + 7m⁵ + 6m⁴ +18)

7m⁵ +11m⁴ - 4m³ + m + 14

Subtracting

100

(4h - 12) - (2h + 8)

2h - 20

200

(4r² + r + 6) - (2r² - 6)

2r² + r + 12

300

(6x² + 5x + 3) - (2x² - 4x + 7)

4x² + 9x - 4

400

(7 - 13x³ - 11x) - (2x³ + 8 - 4x⁵)

4x⁵ - 15x³ - 11x - 1

500

(4x² - 2x + 7) - (-2x² + x - 3)

6x² - 3x + 10

Multiplying

100

2x (3x - 1)

6x² - 2x

200

(3x - 2)(5x - 1) 

15x² - 13x + 2

300

(2x + 5)²

4x² + 20x + 25

400

(x - 10)²

x² - 20x + 100

500

(x + 5)(x² + 3x + 2)

x³ + 8x² + 17x + 10

Dividing

100

x² + 5x - 24 / (x - 3)

x + 8

200

6x² + 11x - 10 divided by 3x - 2

2x + 5

300

6n² - 4n - 16 divided by n - 2

6n + 8

400

x² - 6x + 11 divided by x - 4

x-2 + (3/ x-4)

Remainder Theorem

100

Is x + 1 a factor of x³ - 7x² - 11x - 3?

yes.

200

Is x - 3 a factor of x² - 11x + 24

yes.

300

Is x + 5 a factor of 2x² + 9x - 2?

no.

400

What is the remainder when the polynomial x² - 5x + 3 is divided by the binomial (x-8)?

27

500

What is the remainder when the polynomial x² - 11x + 22 is divided by x-9?

4