Math / Algebra

QuestionSolve. $\begin{array}{l} y^{3}-8 y^{2}-9 y=0 \\ y=\square \end{array}$ $\square$ (Use a comma to separate answers as needed.)

Studdy Solution

STEP 1

What is this asking? We need to find the values of $y$ that make the equation $y^3 - 8y^2 - 9y = 0$ true. Watch out! Don't forget to check if zero is a solution!

STEP 2

1. Factor out the common term
2. Factor the quadratic
3. Solve for $y$

STEP 3

Alright, let's kick things off by noticing that each term in our equation has a $y$ !
That means we can factor it out!
Think of it like reverse distribution.
We're pulling out the common factor to simplify things.
This gives us: $y \cdot (y^2 - 8y - 9) = 0$ Why did we do this?
Because now we have a much simpler equation to work with!

STEP 4

Now, we're left with a quadratic expression inside the parentheses: $y^2 - 8y - 9$ .
Let's factor this bad boy!
We're looking for two numbers that multiply to $-9$ and add up to $-8$ .
Think, think, think... How about $-9$ and $+1$ ?
Yep, those work!
So, we can rewrite the quadratic as: $(y - 9) \cdot (y + 1)$ So, our original equation becomes: $y \cdot (y - 9) \cdot (y + 1) = 0$ Boom! Fully factored!

STEP 5

Now, here comes the grand finale!
We have three factors multiplied together that equal zero.
This means at least one of the factors must be zero.
So, we set each factor equal to zero and solve for $y$ : $y = 0$ $y - 9 = 0 \implies y = 9$ $y + 1 = 0 \implies y = -1$

STEP 6

So, the solutions to our equation are $y = 0$ , $y = 9$ , and $y = -1$ .
We write this as: $y = -1, 0, 9$

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QuestionSolve. $\begin{array}{l} y^{3}-8 y^{2}-9 y=0 \\ y=\square \end{array}$ $\square$ (Use a comma to separate answers as needed.)

Studdy Solution

STEP 1

What is this asking? We need to find the values of $y$ that make the equation $y^3 - 8y^2 - 9y = 0$ true. Watch out! Don't forget to check if zero is a solution!

STEP 2

1. Factor out the common term
2. Factor the quadratic
3. Solve for $y$

STEP 3

STEP 4

STEP 5

Now, here comes the grand finale!
We have three factors multiplied together that equal zero.
This means at least one of the factors must be zero.
So, we set each factor equal to zero and solve for $y$ : $y = 0$ $y - 9 = 0 \implies y = 9$ $y + 1 = 0 \implies y = -1$

STEP 6

So, the solutions to our equation are $y = 0$ , $y = 9$ , and $y = -1$ .
We write this as: $y = -1, 0, 9$

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QuestionSolve. y3−8y2−9y=0y=□\begin{array}{l} y^{3}-8 y^{2}-9 y=0 \\ y=\square \end{array}y3−8y2−9y=0y=□​ □\square□ (Use a comma to separate answers as needed.)

Studdy Solution

STEP 1

What is this asking? We need to find the values of yyy that make the equation y3−8y2−9y=0y^3 - 8y^2 - 9y = 0y3−8y2−9y=0 true. Watch out! Don't forget to check if **zero** is a solution!

STEP 2

1. Factor out the common term2. Factor the quadratic3. Solve for yyy

STEP 3

STEP 4

STEP 5

STEP 6

So, the **solutions** to our equation are y=0y = 0y=0, y=9y = 9y=9, and y=−1y = -1y=−1.We write this as: y=−1,0,9y = -1, 0, 9y=−1,0,9

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionSolve. $\begin{array}{l} y^{3}-8 y^{2}-9 y=0 \\ y=\square \end{array}$ $\square$ (Use a comma to separate answers as needed.)

What is this asking? We need to find the values of $y$ that make the equation $y^3 - 8y^2 - 9y = 0$ true. Watch out! Don't forget to check if zero is a solution!

1. Factor out the common term
2. Factor the quadratic
3. Solve for $y$

So, the solutions to our equation are $y = 0$ , $y = 9$ , and $y = -1$ .
We write this as: $y = -1, 0, 9$