Polynomials Review

Classify the following

100

3x⁵

T:monomial, D:5, LC: 3, SF: 3x⁵

200

-5+4x²

SF: 4x-5, T: binomial, D:2, LC:-5

300

3x²+4x⁶-2

SF: 4x⁶+3x²-2, T: trinomial, D: 6, LC:4

400

3x⁴y³z²

SF: done, T: monomial, D: 8, LC:3

500

4x²-24-x¹²

SF: -x¹²+4x²-24, T:trinomial, D:12, LC-1

Add the polynomials

100

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

3x-2

200

(6x²-2)+(x²-2x-1)

7x²-2x-3

300

(2x+4)+(4x-3+x²)

x²+6x+1

400

(2x⁵+3x²)+(3x⁴+2x²)

2x⁵+3x⁴+5x²

500

(3-2x⁴+3x²)+(x²-x³+12)

-2x⁴-x³+x²+15

Subtract the polynomials

100

(3x²)-(2x²+x)

x²-x

200

(3x+4)-(2x+3)

x+1

300

(3x-4)-(x²-4x-2)

-x²+7x-2

400

(2x+3)-(7x²-3x+2)

-7x²+5x+1

500

(4x²+3x-2)-(2x²-x+8)

2x²+4x-10

Multiply the polynomials

100

2xy(4x²y)

8x³y²

200

(x²-3)(x-4)

x³-4x²-3x+12

300

(x+1)(x²+x+1)

x³+2x²+2x+1

400

(2x+3)(3x³-2x+2)

6x⁴+9x³-4x²-2x+6

500

(x+2)(6x²-3x+4)

6x³+9x²-2x+8

Put it all together

100

(2x)(3x²)+(x³-3)

7x³-3

200

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

-3x²-x-3

300

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

4x²+4x

400

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

2x²+3

500

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

-2x²-5x+1