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. \newlineq3+r3=(q+r)(_____)q^3 + r^3 = (q + r)(\_\_\_\_\_)

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. \newlineq3+r3=(q+r)(_____)q^3 + r^3 = (q + r)(\_\_\_\_\_)
  1. Apply Sum of Cubes Formula: To factor q3+r3q^3 + r^3, we use the sum of cubes formula: a3+b3=(a+b)(a2−ab+b2)a^3 + b^3 = (a + b)(a^2 - ab + b^2).
  2. Identify 'a' and 'b': Let's identify 'a' and 'b' in our expression. Here, a=qa = q and b=rb = r.
  3. Plug in Values: Now, plug in qq and rr into the sum of cubes formula: (q+r)(q2−qr+r2)(q + r)(q^2 - qr + r^2).
  4. Find Quadratic Polynomial: So, the quadratic polynomial that completes the factorization is q2−qr+r2q^2 - qr + r^2.

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 2 months ago

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

Posted 2 months ago

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

Posted 1 month ago

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

Posted 2 months ago

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

Posted 2 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 2 months ago

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

Posted 2 months ago

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

Posted 2 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 2 months ago

View all (35)