Polynomial Equations And Inequalities

Question 1

Long division steps

(x^3 + 4x^2 - 16x - 14) by (x + 1)

Answer 1

1. Divide x^3 by x = x^2
2. Multiply (x+1) by x^2 = x^3 + x^2 (write below)
3. Subtract, bring down next term
4. Divide 3x^2 by x = 3x
5. Multiply (x+1) by 3x = 3x^2 + 3x (write below)
6. Subtract, bring down next term
7. Divide -19x by x = -19
8. Multiply (x+1) by -19 = -19x - 19 (write below)
9. Subtract

Question 2

Quotient form

Answer 2

x^2 - x + 3 + 2/x-1

Question 3

Remainder form

Answer 3

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

Question 4

Remainder theorem explained

Answer 4

Polynomial function P(x) is divided by (x - b) = P(b)

Question 5

Synthetic division

Answer 5

Do a practice question

Question 6

How to do rational zero theorem? (B/A)

Answer 6

Leading coefficient isn’t 1 then:
B = factor of the constant term of P(x)
A = factor of the leading coefficient of P(x)

Question 7

If polynomial equation is facotorable how do you determine roots

Answer 7

By factoring duhhhhh (set factors to zero, solve each factor)

Question 8

If the polynomial equation isn’t factorable how do you find the roots

Answer 8

Determine by a graph

Question 9

What makes functions are “family of polynomial functions”

Answer 9

Family of polynomial functions = all polynomial functions share same characteristics

MUST HAVE BOTH:
- same degree
- same zero of same order

Question 10

Factored general form

Answer 10

F(x) = k(x - x1)…(x - xn)

Question 11

Simplified general

Answer 11

F(x) = k(x^n + bn-1 • x^n-1 + b1 • x + b0)

Question 12

What is the corresponding statement that can be used to check division

Answer 12

Textbook pg 91, 1c

Question 13

If asking to solve

F(x) > 0 and no graph?

Answer 13

Make interval table (must be in factored form)

Question 14

Write the binomial factor that corresponds to the polynomial P(4) = 0

Answer 14

X - 4

Question 15

Factor:

A^3 + B^3

Answer 15

(a+b)(a^2-ab+b^2)

Question 16

Factor:

A^3 - B^3

Answer 16

(a-b)(a^2+ab+b^2)