Question

MEDAL REWARDED
Find the zeros of the function.
f(x) = 9x3 + 36x2 + 27x

Answer 1

@John_ES

Answer 2

When it says to find the "zeroes of the function", it wants you to set \(f(x) = 0\), then solve for \(x\).

In this case,

\(0 = 9x^3 + 36x^2 + 27x\)

Answer 3

You can start off by factoring \(x\) from each term on the right side.

\(0 = x(9x^2 + 36x + 27)\)

Answer 4

Now you have a quadratic in the parentheses that you can factor

Answer 5

Actually, we can factor out 9 as well to get:

\(0 = 9x(x^2 + 4x + 3)\)

Answer 6

That should make the quadratic expression inside the parentheses easier to factor.

Answer 7

And then what? sorry i learn better when someone just does the whole thing and then i look at their steps

Answer 8

So next we have to factor the quadratic expression inside the parentheses:

\(x^2 + 4x + 3\)

Can you factor that or no?

Answer 9

uhm you can take an x out right?

Answer 10

You have to find two numbers that multiply to get 3, but also add to get 4

\(m \times n = 3\)
\(m + n = 4\)

Can you guess the two numbers?

Answer 11

1 and 3

Answer 12

is the answer 0, 3, and 1?

Answer 13

You're sort of jumping ahead. You shouldn't

Answer 14

There's a reason we factor first before trying to find x

Answer 15

Im just trying to find the answer real fast so i can see if i got it right in my review.

Answer 16

You found the two numbers, so now we will replace 4 with 3 + 1 in the quadratic \(x^2 + 4x + 3\) to get:

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

Then distribute the x:

\(x^2 + 3x + x + 3\)

Now notice that we can factor \(x\) from the first two terms, and 1 from the least two terms:

\(x(x + 3) + 1(x + 3)\)

And now (x + 3) is the remaining common factor so:

\((x + 3)(x + 1)\)

Answer 17

So now....that we put that back in place of the quadratic:

\(0 = x(x + 3)(x + 1)\)

Answer 18

Can you see what the values of x are now?

Answer 19

so its just 3 and 1

Answer 20

No, the next step is to take each term and set it equal to zero using the zero product property:

x = 0
x + 3 = 0
x + 1 = 0

Obviously x = 0 is one of the solutions. Try solving for x for the other two.

Answer 21

oh yeah duh, 0, -3, -1

Answer 22

it's okay to be able to figure out (in the end) what the answer is, but you should try to learn how to do ALL the steps.