Polynomials

Adding and Subtracting Polynomials

100

Find the sum:

x² + x + 1 + (x² + x + 1)

2x² + 2x + 2

200

Find the sum:

(4x² + 2x − 3) + (5x² + 3x + 1)

9x² + 5x - 2

300

Find the difference:

(4x² − 6x + 4) - (x² + x − 7)

3x² - 7x + 11

400

Find the sum:

(-2x⁸ - 1) + (8x² - 3x + 1)

-2x⁸ + 8x² - 3x

500

Find the difference:

(7x³ - x² + 3x) - (5x³ + 6x² - 3x - 10)

2x³ - 7x² + 6x + 10

Multiplying Polynomials

100

Find the product:

-3y²(8y² - y + 10)

-24y⁴ + 3y³ - 30y²

200

Find the product:

(x + 9)(x - 3)

x² + 6x - 27

300

Find the product:

(3x + 7)(3x - 7)

9x² - 49

400

Find the product:

(2x² - 1)(x² + 4x + 5)

2x⁴ + 8x³ +9x² - 4x - 5

500

Find the product:

(x² + 2x + 1)(x² + 2x + 1)

(x + 1)⁴

^OR

x⁴ + 4x³ + 6x² + 4x + 1

GCFs

100

Find the GCF:

4x² - 4

4

200

Find the GCF:

6x²y³ + 12xy² + 9xy 

3xy

300

Find the GCF:

3y² - 5y + 7

1

400

Rewrite as the product of the GCF and a polynomial.

8x³ - 4x² + 30x

2x(4x² - 2x + 15)

500

Rewrite as the product of the GCF and a polynomial:

4m²x²y³ - 400m²y³

4m²y³(x² - 100)

or,

4m²y³(x - 10)(x + 10)

Factoring

100

Factor:

x² - 3x - 10

(x - 5)(x + 2)

200

Factor

36y² - 1

(6y + 1)(6y - 1)

300

Factor:

3x² - 16x + 5

(3x - 1)(x - 5)

400

Factor:

4y² − 12y + 9

(2y - 3)²

or

(2y - 3)(2y - 3)

500

Factor:

6y² + 9y - 15

3(y-1)(2y + 5)

Miscellaneous

100

What pair of factors of −45 has a sum of 4?

9 and -5

200

What is the prime factorization of 140?

That is, what prime numbers multiply to make 140?

2*2*5*7

300

Describe the following with its degree and polynomial name:

 3y³ + 3x³y⁴

7th degree binomial

400

Write in standard form:

3x³ − 5x + 7x⁴ − 9 − x²

 7x⁴ + 3x³ − x² − 5x − 9

500

Add the following polynomials. Then determine the GCF:

(3x² - 2x + 7) + (x² + 32x - 7)

4x² + 30x

GCF = 2x