Login
Premium
Home Question Bank Math Algebra
Question

Factor completely: \( x^{3} - 6x^{2} + 9x \)

Ask by Bowman Erickson. in Pakistan
Nov 30,2024

Real Tutor Solution

Tutor-Verified Answer

Answer

\( x(x-3)^{2} \)

Solution

Factor the expression \( x^3 - 6x^2 + 9x \). Factor the expression by following steps: - step0: Factor: \(x^{3}-6x^{2}+9x\) - step1: Factor the expression: \(x\left(x^{2}-6x+9\right)\) - step2: Factor the expression: \(x\left(x-3\right)^{2}\) The completely factored form of \( x^{3} - 6x^{2} + 9x \) is \( x(x-3)^{2} \).

Reviewed and approved by the UpStudy tutoring team

error msg
Explain
Simplify this solution

Mind Expander

To factor \( x^{3} - 6x^{2} + 9x \) completely, the first step is to factor out the greatest common factor (GCF), which is \( x \). This gives us: \[ x(x^{2} - 6x + 9) \] Next, we can focus on factoring the quadratic expression \( x^{2} - 6x + 9 \). Notice that this can be factored as: \[ x^{2} - 6x + 9 = (x - 3)(x - 3) = (x - 3)^2 \] So, the complete factorization of the original expression is: \[ x(x - 3)^{2} \]

Related Questions

2) \( a^{2}-11 a-12 \)
Algebra South Africa Jan 22, 2025
An electrician charges an initial fee of \( \$ 50 \) and \( \$ 190 \) after 4 hours of worl a. Write a linear model that represents the total cost as a function of the \[ y=35 x+50 \] b. How much does the electrician charge per hour? \[ 4 x+x=140+5= \]
Algebra United States Jan 22, 2025
1. Find the products. a) \( (x+2)(x+3) \) c) \( (a-2)(a+3) \) e) \( (2 y+5)(3 y-2) \) g) \( (2 a-3)(3 a-2) \) i) \( (x-3)(x-2) \) k) \( (2 x-3 y)(2 x+4 y) \) m) \( (7 x+3 y)(2 x-4 y) \)
Algebra South Africa Jan 22, 2025
7 Expand and simplify \( 5 x(3 x+4)(2 x-1) \)
Algebra United Arab Emirates Jan 22, 2025
4. \( \frac{2 x-1}{3}-\frac{4 x-8}{6} \) 6. \( \frac{3}{x-1}+\frac{1}{1-x} \) 8. \( \frac{x}{x+y}+\frac{y}{x-y} \) 10. \( \frac{x+3}{x-3}-\frac{x-3}{x+3} \) 12. \( \frac{5}{3(a-b)}+\frac{3}{2(b-a)} \) 14. \( \frac{x}{x^{2}-y^{2}}+\frac{y}{y^{2}-x^{2}} \) 16. \( \frac{4 x}{(x+y)^{2}}-\frac{4}{x+y} \) 18. \( \frac{3 a}{9 a^{2}-4 b^{2}}-\frac{1}{3 a+2 b} \) 20. \( \frac{2 y}{(x-2 y)^{2}}+\frac{1}{x-2 y} \)
Algebra United States Jan 22, 2025

Latest Algebra Questions

2. Find the products. \( \begin{array}{ll}\text { a) }(x+1)(x+3) & \text { b) }(a+3)(a+4) \\ \text { c) }\left(x^{2}-1\right)\left(2 x^{2}+3\right) & \text { d) }\left(a^{2}-2\right)\left(a^{2}+2\right) \\ \text { e) }(3 x y+2 z)(2 x y-3 z) & \text { f) }(p r+2 t)(3 p r-t) \\ \text { g) }\left(x^{2}-4\right)\left(4 x^{2}-3\right) & \text { h) }\left(2 a^{2}+1\right)\left(3 a^{2}+1\right) \\ \text { i) }\left(x+\frac{1}{2}\right)\left(x+\frac{1}{4}\right) & \text { j) }\left(2 x+\frac{1}{3}\right)\left(3 x-\frac{1}{2}\right) \\ \text { k) }(2 a-b)(2 a+b) & \text { l) }(3 x+2 y)(3 x-2 y) \\ \text { m) }\left(\frac{1}{2} x+\frac{1}{3} y\right)\left(\frac{1}{3} x-\frac{1}{2} y\right) & \text {-n) }(x+3)^{2}\end{array} \)
Algebra South Africa Jan 22, 2025
5. \( \begin{aligned} j-9 \pi= & 12 \pi \\ +9 \pi & +9 \pi\end{aligned} \)
Algebra United States Jan 22, 2025
7 Expand and simplify \( 5 x(3 x+4)(2 x-1) \)
Algebra United Arab Emirates Jan 22, 2025
1. Find the products. \( \begin{array}{ll}\text { a) }(x+2)(x+3) & \text { (b) }(p-3)(p-4) \\ \text { c) }(a-2)(a+3) & \text { d) }(2 x-3)(3 x+1) \\ \text { e) }(2 y+5)(3 y-2) & \text { f) }(3 a-7)(2 a+1) \\ \text { g) }(2 a-3)(3 a-2) & \text { (h) }(4 y+1)(7 y-2) \\ \text { i) }(x-3)(x-2) & \text { j) }(4 a-2)(3 a+5) \\ \text { k) }(2 x-3 y)(2 x+4 y) & \text { 1) }(2 a-7 b)(3 a-2 b) \\ \text { m) }(7 x+3 y)(2 x-4 y) & \text { n) }(3 a-2 b)(2 a+11 b)\end{array} \)
Algebra South Africa Jan 22, 2025
1. Find the products. \( \begin{array}{ll}\text { a) }(x+2)(x+3) & \text { \b) }(p-3)(p-4) \\ \text { c) }(a-2)(a+3) & \text { d) }(2 x-3)(3 x+1) \\ \text { e) }(2 y+5)(3 y-2) & \text { f) }(3 a-7)(2 a+1) \\ \text { g) }(2 a-3)(3 a-2) & \text { (h) }(4 y+1)(7 y-2) \\ \text { i) }(x-3)(x-2) & \text { j) }(4 a-2)(3 a+5) \\ \text { k) }(2 x-3 y)(2 x+4 y) & \text { \l) }(2 a-7 b)(3 a-2 b) \\ \text { m) }(7 x+3 y)(2 x-4 y) & \text { n) }(3 a-2 b)(2 a+11 b) \\ \text { 2. Find the products. } & \text { b) }(a+3)(a+4) \\ \text { a) }(x+1)(x+3) & \text { (d) }\left(a^{2}-2\right)\left(a^{2}+2\right) \\ \text { c) }\left(x^{2}-1\right)\left(2 x^{2}+3\right) & \text { f) }(p r+2 t)(3 p r-t) \\ \text { (e) }(3 x y+2 z)(2 x y-3 z) & \text { h) }\left(2 a^{2}+1\right)\left(3 a^{2}+1\right) \\ \text { g) }\left(x^{2}-4\right)\left(4 x^{2}-3\right) & \text { j) }\left(2 x+\frac{1}{3}\right)\left(3 x-\frac{1}{2}\right) \\ \text { i) }\left(x+\frac{1}{2}\right)\left(x+\frac{1}{4}\right) & \text { l) }(3 x+2 y)(3 x-2 y) \\ \text { k) }(2 a-b)(2 a+b) & \text { n) }(x+3)^{2} \\ \text { m) }\left(\frac{1}{2} x+\frac{1}{3} y\right)\left(\frac{1}{3} x-\frac{1}{2} y\right) & \end{array} \)
Algebra South Africa Jan 22, 2025
Prev Next
Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy