Grade 9 Math Polynomial Review

Adding Polynomials

100

Add the Polynomials

(4x + 9) +(x - 4)

5x + 5

200

Add the polynomials:

(-3a - 2) + (7a + 5)

4a + 3

300

Add the polynomials:

(x² +3x + 5) + ( -x² +6x)

9x + 5

400

Add the polynomials:

(t² + 3t³ -3) + (2t² +7t -2t³) 

t³ +3t² +7t -3

500

Add the polynomials: 

(-1 + x² + 2x) + (1 -2x + 2x²)

3x²

600

Find the perimeter of a triangle whose side lengths are 3x, 2x + 7,  and 18 units long.

5x + 25 units

Subtracting Polynomials

100

Subtract the polynomials:

(g - 4) - (3g - 6)

-2g + 2

200

Subtract the polynomials:

(-5h - 2) - (7h +6)

-12h - 8

300

Subtract the polynomials:

(-x² - 5) - (-3x² -x -8)

2x² + x +3

400

Subtract the Polynomials:

(k² + 6k³ -4) - (5k³ + 7k -3k²)

k³ + 4k² -7k -4

500

Subtract the Polynomials:

(2x - 3x) - (x² -2x + 4)

-x² + x - 4

600

Subtract the following polynomials

(3 - 6x⁵ - 8x⁴) - (-6x⁴ - 3x - 8x⁵)

2x⁵ - 2x⁴ + 3x + 3

factoring out the GCF

100

Factor out the GCF

m² – 2mn

m(m – 2n)

200

Factor out the GCF

10a⁸ +20a⁶

10a⁶(a²+2)

300

Factor out the GCF

-24c⁶ – 32c⁴

-8c⁴(3c² + 4)

400

Divide the polynomial:

18r⁵ + 36r⁴ + 27r³ 

9r³(2r² + 4r + 3) 

500

Factor out the GCF

34m³n² – 51m²n³ 

17m²n²(2m – 3n)

600

Divide the Polynomials:

3x³y + 6x² y - 9x²

3x²(xy+2y-3)

Multiplying Polynomials

100

Multiply the Polynomials:

3x² (2x⁴)

6x⁶

200

Multiply the Polynomials:

3(2x + 4x² - 5)

12x² + 6x - 15

300

Multiply the Polynomials:

−y² (−8x² − 6xy − y² )

8y²x² + 6y³x + y⁴ 

400

Multiply the Polynomials:

(x-2)(x+6)

x²+4x-12

500

Multiply the Polynomials:

(3x-6)(5x+3)

15x²-21x-18

600

Multiply the following polynomials

(3r+ 5)²

9r² + 30r + 25

Factoring

100

Factor completely

7p³+7p² - 5p - 5

.

(7p² - 5)(p+1)

200

Factor completely

x² + 10x + 21

(x + 7)(x + 3)

300

Factor completely

4x² + 4x - 3

(2x - 1)(2x + 3)

400

Factor completely

18n² - 21n + 6 

3(3n - 2)(2n - 1)

500

Factor completely

5p² - 25p + 20

5(p - 4)(p - 1)

600

21b³ + 6b² - 14b - 4

(3b² - 2)(7b + 2)