5.3,5.5-5.6

Question 1

What must be in order to use sum or differences of cubes?

Answer 1

must be cubed; also a two part formula

Question 2

Sum or Difference of Cubes Formula

Answer 2

a3 + b3 = (a + b)(a2 – ab + b2)

a3 – b3 = (a – b)(a2 + ab + b2)

Question 3

General Steps in sum or difference of cubes

Answer 3

divide by square root of 3 
use the resulting numbers for a and b respectively
plug into formula
solve binomial
quadratic formula

Question 4

roots (also referred to as)

Answer 4

solutions of a polynomial equation (zero/solution/x-intercept)

Question 5

Fundamental Theorem of Algebra

Answer 5

the degree (highest power) of a polynomial tells how many solutions exist

Question 6

conjugate root theorem

Answer 6

all irrational and complex numbers come in pairs

Question 7

rational root theorem

Answer 7

for the real roots of a polynomial equation, a list of possible solutions can be created in the form ;
+ factors of the constant term (last)
- factors of the leading coefficient (first)

Question 8

Main Method

Answer 8

Graph to find rational roots, use those zeros in synthetic division to reduce the powers to a square, and solve the remaining quadratic equation by the quadratic formula

Question 9

in synthetic division, each new repeat

Answer 9

the x value goes down 1 power

Question 10

to solve a polynomial equation it must equal

Answer 10

zero

Question 11

solve by factoring

Answer 11

divide out GCF if necessary, factor the quadratic or perfect quartic equation using the ac/b chart , set factor equal to zero and solve. (if factoring didn’t work use quadratic formula) #set GCF to 0

Question 12

i squared

Answer 12

-1

Question 13

i cubed

Answer 13

-i

Question 14

For the bonus, with squares and is and halves

Answer 14

just use foil and multiply

Question 15

foiling for conjugates

Answer 15

only foil first and last, postitive I times -I=positive number

Question 16

when checking the result of the quadratic

Answer 16

should be split

Question 17

a polynomial with real coefficients has roots of 6,-2,-4i, and the square root of 5

Answer 17

negative square root of 5, 4i= all conjugates need a pair

Question 18

list one method of solving this polynomial that works and why. Then list one method that doesn’t work and why. (5 part)

Answer 18

cube root won’t work because you can’t cube root all these numbers
not 3 terms;unfactorable
Main method works because the calc. gives numbers and you can use synthetic division to find rest

Question 19

What is quadratic formula and why is it used when solving some polynomials

Answer 19

once you have used synthetic division (or is unfactorable) it will show imaginary or irrational roots

Question 20

Is it possible to solve a polynomial by factoring using difference of cubes and difference of squares? Provide an example

Answer 20

Yes,(x squared-4) (x cubed-8)=x to the 5th+4x cubed+8x squared+32

Question 21

when do u factor

Answer 21

when it is a trinomial and the powers are 4,2,0

Question 22

how you can find a possible root

Answer 22

rational root theorem

Question 23

explain which process you might try if the polynomial had

Answer 23

2-main method, sum/difference of cubes or squares
3-main method, GCF/factoring, power 4,2,0
4-main method

Question 24

explain the relationship between an x-intercept, a factor, and synthetic division

Answer 24

factor is solution to equation. when solve, factor is an x-intercept. to check that a factor is a solution we use synthetic division to check its remainder. If the remainder is 0 the factor is an x-intercept