Polynomials

Exponent Rules

100

x²*x⁵

x⁷

200

Simplify : (2x²)³

8x⁶

300

Rewrite with positive exponents: 

-3x^-3

-3/x^3

400

Rewrite with positive exponents: 

(1/2 x^3)^-4

16/x^12

500

Simplify 

(-4x)^3(x^7y^4)^5(2xy)^-2

-16x^36y^18

Adding Polynomials

100

Add the Polynomials

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

5x + 5

200

Add the polynomials:

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

4a + 3

300

Subtract the polynomials:

(-x² - 5) - (-3x² -x -8)

2x² + x +3

400

Add the polynomials:

(t² + 3t³ -3) + (2t² +7t -2t³) 

t³ +3t² +7t -3

500

Subtract the Polynomials:

(2x - 3x) - (x² -2x + 4)

-x² + x - 4

Multiplying Polynomials

100

Multiply the Polynomials:

3x² (2x⁴)

6x⁶

200

Multiply the Polynomials:

(x - 3)(x + 2)

x² - x - 6

300

Multiply the Polynomials:

(2m - 1)(m + 2)

2m² + 3m - 2

400

Multiply the Polynomials:

(4n - 1)(3n + 4)

12n² + 13n - 4

500

Multiply the Polynomials:

(2x - 3)(x² + 3x + 2)

2x³ + 3x² - 5x - 6

Polynomial Definitions

100

What is the coefficient of 3x²?

3

200

What is the degree of the polynomial?

4x³-3x²+2x-100

3

300

How many terms does the polynomial have?

4x³-3x²+2x-100

4

400

Classify the polynomial by the degree & number of terms:

7x-5x²-3x⁵

degree 5 trinomial

500

After fully simplifying, classify the polynomial by its degree and number of terms:

(3x)²+3x-7x²+18x-2x²

Degree 1 (linear) monomial

synthetic and long division

100

Is x+3 a factor of  x²+5x+1

NO

200

Is x-5 a factor of x³-125? If yes, name the remaining solutions (real and imaginary)

Yes  5, -5 plus and minus 5 i root 3 over 2

300

Is x-1 a factor of 5x⁴+2x²-7x?  Name all real and imaginary solutions

yes, 0,1, -5 + i root 115 over 10, -5-i root 115 over 10

400

Name all the solutions of 2x³-11x²+13x

0, 11 plus and minus root 17 over 4

500

(2p²+7p-39) / (2p-7)

p+7 + 10/(2p-7)