Adding, Subtracting, and Classifying Polynomials

Adding

100

Add.

(2x² + 6x + 5) + (3x² - 2x - 1)

5x² + 4x + 4

200

Add.

(5x²+8x-10)+(-12-x+3x²)

8x²+7x-22

300

Add.

(3x² - 6x + xy) + (7x + 8y)

3x²+x+xy+8y

400

Add. 

(8x-x³+4-9x²)+(7x³+9x²-10-8x)

6x³-6

500

P = 3x² + xy - 5y², Q = 2x² - xy + 3y² and R = -6x² + 4xy - 7y² What is P + (Q + R) ?

-x²+4xy-9y²

Multiplying Polynomials

100

(5a²b⁵)(7a⁴b^-3)

35a⁶b²

200

(2x-5)²

4x²-20x+25

300

4x(x-3)(x+4)

4x³+4x²-48x

400

(x-4)(x²+3x+7)

x³-x²-5x-28

500

2x(x+5)(x-3)²

2x⁴ - 2x³ - 42x² + 90x

Classify Polynomials

100

Classify the polynomial by degree and number of terms. 

x - 4

Linear binomial

200

Classify the polynomial by degree and number of terms. 

-7

Constant monomial

300

Classify the polynomial by degree and number of terms. 

5-6x³+4x

Cubic trinomial

400

Classify the polynomial by degree and number of terms. 

-1+7x²+4x³+9x

Cubic polynomial

500

4x²-4x²+3x⁴-5x²+x⁴

Quartic binomial

Standard Form and Factoring

100

Completely Factor the polynomial

x⁴-5x+4

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

200

Rewrite the polynomial in standard form. 

8x-2-6x³

-6x³+8x-2

300

Rewrite the polynomial in standard form. 

5x³+14x+7x²+3x-11-2x²

5x³+5x²+17x-11

400

Factor the polynomial

5x⁴+135x

5x(x+3)(x²-3x+9)

500

Write in simplified standard form

-3x²+4x-7x³+8+5x²

-7x³+2x²+4x+8

Subtract

100

Subtract. 

(2x²-2x+3)-(x²+5x-5)

x²-7x+8

200

Subtract.

 (2x² - 4y + 7xy - 6y²) - (-3x² + 5y - 4xy + y²)

5x² - 7y² -9y + 11xy

300

Subtract. 

(7x²+11-5x) - (3x²+2x-11)

4x²-7x+22

400

If P = 5x⁴ - 2x² + 4x - 3 and Q = 5x⁴ + 3x³ - 4x + 3, what is P - Q?

What is -3x³ - 2x² + 8x - 6

500

Subtract. 

(x-2x³+8-7x²) - (8+5x-3x³)

x³-7x²+x