Polynomials & Literal Equations

Adding/Subtracting Polynomials

100

Add the following polynomials

x⁴+4x⁴

5x⁴

200

Add the following polynomials

(x²-3)+(3x²+7)

4x²+4

300

Subtract the following polynomials

(a³-2a²)-(4a³+3a²)

-3a³-5a²

400

Add the following polynomials

(-9k³-3k²h+h⁴)+(k³-7kh²+4h⁴)

-8k³-3k²h-7kh²+5h⁴

500

Subtract the following polynomials

(3-6n⁵-8n⁴)-(-6n⁴-3n-8n⁵)

2n⁵-2n⁴+3n+3

Multiplying Polynomials

100

Multiply the following polynomials

w²(w²+3)

w⁴+3w²

200

Multiply the following polynomials 

r²(7r³-3r+9)

7r⁵-3r³+9r²

300

Multiply the following polynomials

(9m-3)(2m+3)

18m²+21m-9

400

Multiply the following polynomials

(3r²+5)²

9r⁴+30r²+25

500

Multiply the following polynomials

(t²+4)(t³+6r-3)

t⁵+6t²r+4t³-3t²+24r-12

Factoring Polynomials

100

Factor the polynomial

15g³-5g

5g(3g²-1)

200

Factor the polynomial

3g⁵+9g³-18g²

3g²(g³+3g-6)

300

Factor the polynomial 

t²-11t+24

(t-3)(t-8)

400

Factor the polynomial

6x²+x-12

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

500

Factor the polynomial

4x²+22x+10

2(x+1)(x+5)

Polynomial Terminology

100

Name the degree and number of terms of this polynomial: 

x³-7x²+4x⁵-19x⁷

7th degree polynomial in 4 terms

200

Classify this polynomial using degree and number of terms:

2x³+3x-7

Cubic Trinomial

300

Classify by degree and number of terms:

10

Constant Monomial

400

Write the polynomial in Standard form and state the coefficient on the quadratic term.

6x³-3x+12x⁵+x⁴

12x⁵+x⁴+6x³-3x

0 is the coefficient on the quadratic term, 0x².

500

True or False, If false, correct the statement.

Polynomials can have constants, variables and exponents all of which must be integers.

FALSE, Polynomials have real number coefficients and non-zero integer exponents of the form

a_nx^n+a_(n-1)x^(n-1)+...+a_1x+a_0

Literal Equations

100

z=(4a)/3

 solve for a.

 a = (3z) / 4 

200

If u = 3a + 3 , solve for a.

a = (u - 3) / 3

300

u = ka - b , solve for for a.

a = (u + b) / k

400

xm = p - n + yx

Solve for x.

x = (p - n) / (m - y)

500

z = (am + p) / (an)

Solve for a.

a = p / (zn - m)