Question

Which of the following is an x-intercept of the function,
http://media.apexlearning.com/Images/201308/06/0a76cbe9-9bf8-4873-9de4-df062a46d817.gif

A.2
B.-2
C.4
D.-4

Answer 1

You could substitute each of these four possible roots / zeros / x-intercepts / solutions into the given equation and determine whether or not the resulting equation is zero. If yes, then you've found one x-intercept.

Or, you could look at the given polynomial and use your favorite method to factor it.
Personally I'd start with synthetic division.

Answer 2

i got d.

Answer 3

explain why you think d is correct.

Answer 4

I just guessed lol

Answer 5

As you know, that won't work in the long run. Know synth. division?

Answer 6

If not, then please try long division. Divide the given polynomial by (x-4), which stems directly from the possible solution x = 4.

Answer 7

Rule: If you apply either long division or synth. division here, and there's no remainder (other than zero), you've found a root / zero / solution / x-intercept.

any questions?

Answer 8

Oh okay cool. So if there is a remainder in syn. Division it is not a root or x-intercept?

Answer 9

Exactly. Set up synth div. using 4 as your divisor and using the coefficient 1, -5, -8, 48.
______________
5 / 1 -5 -8 48

Answer 10

can you do this synth. div?

Answer 11

Yes

Answer 12

Is there a rem. or not?

Answer 13

Yes there is i got a remainder of 8

Answer 14

My result had a zero remainder. Let's look over what you've done and see why we got different results.

Answer 15

MY MISTAKE!! Divide by 4, not by 5. Sorry. Try again.

Answer 16

Yeah i got 0 as well

Answer 17

Can you help me on another question?
Which polynomial function is graphed below?
http://media.apexlearning.com/Images/201309/30/af7451cb-1fab-49c7-9c89-685ffe52f350.JPG
A. f(x)=(x-2)^2(x+3)
B. f(x)=(x-2)(x+3)^2
C. f(x)=(x-3)(x+2)^2
D. f(x)=(x-3)^2(x+2)

Answer 18

Cool. that means that 4 is a factor of the given polynomial.
Your quotient is x^2 - x - 12, which has factors of its own, but you were asked only to pick the one possible solution out of 4 given.

Answer 19

I can see immediately that one root of the given poly is -2 and that the other is 3. Be sure you know where these numbers came from.

this info should help you eliminate 1 or 2 of the possible answers.

Answer 20

The possible answers are either a or b?

Answer 21

Actually, the non-answers are a or b. See if you can figure out why this is. Note the signs of the 2 and 3.

Answer 22

Bc the two is going up and 3 is going down right?

Answer 23

It is D?