Question

Medal/fan? :)

Will you guys check my work? Also, I need help on two questions.

Need Help:

Given the binomials (x - 2), (x - 1), (x + 2), and (x - 4), which one is a factor of f(x) = x3 + 7x2 + 14x + 8?

(x - 2)

(x - 1)

(x + 2)

(x - 4)

Given the binomials (x + 1), (x + 4), (x - 5), and (x - 2), which one is a factor of f(x) = 3x3 - 12x2 - 4x - 55?

(x + 1)

(x + 4)

(x - 5)

(x - 2)

Answer 1

it would take some time ... to solve

Answer 2

ok it is pretty simple .....

Answer 3

Check My Work:

What is the f of x over the g of x when f(x) = 6x3 - 19x2 + 16x - 4 and g(x) = x - 2?

6x2 - 7x + 2 (My answer)

3x2 - 9x + 8

6x2 - 7x + 2 - 8 over the quantity of x minus 2

3x2 - 9x + 8 - 8 over the quantity of x minus 2



What is the quotient when -3x3 + 5x + 14 is divided by x - 2?

-3x2 - 6x - 7

- 3x2 - x + 12 (My answer)

-3x2 + 6x - 7 + 28 over the quantity of x minus 2

-3x2 - x + 12 + 28 over the quantity of x minus 2

What is the quotient when x3 - 5x2 + 2x + 5 is divided by x - 2?

x2 - 3x - 4

x2 - 7x + 16

x2 - 3x - 4 - 3 over the quantity of x minus 2 (my answer)

x2 - 7x + 16 - 3 over the quantity of x minus 2

Answer 4

why dont you just plug in the values of 2 ,1 , -2,-4 in the first question and see which one comes out as zero

Answer 5

i think that is the simplest way to get it
okay first you plug in 2

Answer 6

you wont get it with 1 and 2 ... now for he negative values ..

Answer 7

for the first one i would say x+2
do you know what is a factor ? it is something which when put to a equation you would get zero on the other side ...

Answer 8

just use the factor theorem

if (x -2) is a factor then f(2) = 0

saves a lot of solving... it just requires substitution... whichever values, when substituted returns a zero, then that is a zero of the polynomial, and then you have a factor

Answer 9

campbell .. you could help her right?

Answer 10

the 1st question is really straight forward if you know about the zeros of a polynomial...

since every term in the cubic is positive, substituting a positive number will give a positive value...

so start by selecting the binomial factor that would have a negative zero... and try that.

Answer 11

so here is the basics if

(x -2) is a factor x = 2 is a zero

substitute \[f(2) = (2)^3 + 7(2)^2 + 14(2) + 8\]

its a positive answer... so not a factor...

try

(x + 2) which means x - 2 is a zero substitute and check

\[f(-2) = (-2)^3 + 7(-2)^2 + 14(-2) + 8\]

if you evaluate it you'll get f(-2) = 0

so (x + 2) is a binomial factor.

hope this makes sense

Answer 12

it does.

Answer 13

for your 2nd question

(x+ 1) then if x = -1 is a zero show f(-1) = 0

(x +4) then x - 4 is a zero show f(-4) = 0

same process for the other binomial factors...

as you can see, no difficult solving...

hope this helps...

Answer 14

What is the f of x over the g of x when f(x) = 6x3 - 19x2 + 16x - 4 and g(x) = x - 2?

6x2 - 7x + 2 (My answer)

You did this correct (I just took the test)