Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find the quadratic polynomial that completes the factorization. \newliner3−512=(r−8)(_____)r^3 - 512 = (r - 8)(\_\_\_\_\_)

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Precalculusright chevron icon
Factor sums and differences of cubesright chevron icon

Full solution

Q. Find the quadratic polynomial that completes the factorization. \newliner3−512=(r−8)(_____)r^3 - 512 = (r - 8)(\_\_\_\_\_)
  1. Recognize as difference of cubes: To factor r3−512r^3 - 512, recognize it as a difference of cubes: r3−83r^3 - 8^3.
  2. Apply formula for factoring: The formula for factoring a difference of cubes is a3−b3=(a−b)(a2+ab+b2)a^3 - b^3 = (a - b)(a^2 + ab + b^2).
  3. Factor using aa and bb: Apply the formula with a=ra = r and b=8b = 8: (r−8)(r2+8r+64)(r - 8)(r^2 + 8r + 64).
  4. Check the multiplication: Check the multiplication: r - \(8)(r^22 + 88r + 6464) = r^33 + 88r^22 + 6464r - 88r^22 - 6464r - 512512\
  5. Simplify the expression: Simplify the expression: r3+8r2+64r−8r2−64r−512=r3−512r^3 + 8r^2 + 64r - 8r^2 - 64r - 512 = r^3 - 512.

More problems from Factor sums and differences of cubes

Question
Find the degree of this polynomial.\newline`5b^{10} + 3b^3`\newline_______
Get tutor helpright-arrow

Posted 3 months ago

Question
Subtract.\newline(9a+5)−(2a+4)(9a + 5) - (2a + 4)\newline____
Get tutor helpright-arrow

Posted 3 months ago

Question
Find the product. Simplify your answer. \newline−3v2(v2−9)-3v^2(v^2 - 9)\newline________
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the product. Simplify your answer.\newline(v−3)(4v+1)(v - 3)(4v + 1)\newline______
Get tutor helpright-arrow

Posted 3 months ago

Question
Find the square. Simplify your answer.\newline(3y+2)2(3y + 2)^2\newline______
Get tutor helpright-arrow

Posted 3 months ago

Question
Divide. If there is a remainder, include it as a simplified fraction.\newline(24t2+36t)÷6t(24t^2 + 36t) \div 6t\newline______
Get tutor helpright-arrow

Posted 2 months ago

Question
Is the function q(x)=x6−9 q(x) = x^6 - 9 even, odd, or neither?\newlineChoices:\newline[[even][odd][neither]]\text{[[even][odd][neither]]}
Get tutor helpright-arrow

Posted 3 months ago

Question
Find the product. Simplify your answer. \newline−3q2(−3q2+q)-3q^2(-3q^2 + q)\newline______
Get tutor helpright-arrow

Posted 3 months ago

Question
Find the product. Simplify your answer.\newline(r+3)(4r+2)(r + 3)(4r + 2)\newline______
Get tutor helpright-arrow

Posted 3 months ago

Question
Find the roots of the factored polynomial.\newline(x+7)(x+4)(x + 7)(x + 4)\newlineWrite your answer as a list of values separated by commas.\newlinex=x = ____
Get tutor helpright-arrow

Posted 3 months ago

View all (34)