Question

Factoring a polynomial: (see attachment at the very bottom)

Answer 1

and the questions:
(b) find the remaining factors of f

Answer 2

(c) use your results to write the complete factorization of f

Answer 3

(d) list all real zeros of f. confirm your results by using a graphing utility to graph the function

Answer 4

what especially is the "remaining factors of f"?

Answer 5

after they used synthetic division on f(x), they got the numbers 2, -3, 1, and 0 on the bottom, do you understand that part?

Answer 6

yeah i know that that is one of the factors found for the product above (2x^3 + x^2 -5x + 2)

Answer 7

ok, so the numbers

2, -3, 1, and 0

represent the polynomial

(2x^2-3x+1), do you understand that part?

Answer 8

yeah

Answer 9

for part b, they factored

2x^2-3x+1

to get (2x-1)(x-1)

these are called the "remaining factors" because we already figured out that x = -2 is a factor (using synthetic division)

Answer 10

how did they factor that expression?

Answer 11

to get to get (2x-1)(x-1)?

Answer 12

uh, it's sort of a guess-and=check method

Answer 13

so not foil? not grouping? not complete the square?

Answer 14

well, factoring is sort of the reverse of foil

Answer 15

I guess I can tell you a shortcut method to help figure out how a trinomial factors

Answer 16

we have:

2x^2-3x+1

first, we draw a cross

Answer 17

for this unit i struggle with how to factor polynomials - like the guess and check method. how exactly fo you figure that out?

Answer 18

then we look at our polynomial:

2x^2-3x+1

first, we look at the x^2 term. we then look at the coefficient attached to it (2), and list 2 factors of 2, and then write them on the left side of the cross

Answer 19

I'll just go with 1 and 2 since 1*2 = 2

Answer 20

where are the terms of the expression placed on the factor diamond?

Answer 21

oh, I guess you're using the diamond method?

Answer 22

haha that's what i thought you were doing?

Answer 23

mine's a little different, I haven't used the diamond method in a long time

Answer 24

anyway, then I look at the constant (non-variable term) of the expression

2x^2-3x+1

which is 1, so i pick two factors (-1) and (-1)

Answer 25

then I multiply along each line and add the two products