math-algebra

Factor the polynomial

64x^3-27

  1. 👍
  2. 👎
  3. 👁
  1. 64 = 4 ^ 3

    64 x ^ 3 = ( 4 x ) ^ 3

    27 = 3 ^ 3

    64 x ^ 3 - 27 = ( 4 x ) ^ 3 - 3 ^ 3

    a ^ 3 - b ^ 3 = ( a - b ) ( a ^ 2 + a b + b ^ 2 )

    In this case:

    64 x ^ 3 - 27 = ( 4 x ) ^ 3 - 3 ^ 3 = ( 4 x - 3 ) * [ ( 4 x ) ^ 2 + 4 x * 3 + 3 ^ 2 ] =

    ( 4 x - 3 ) * ( 16 x ^ 2 + 12 x + 9 )

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    Find the discriminant for the quadratic equation f(x) = 5x^2 - 2x + 7 and describe the nature of the roots. discriminant is 144, one real root discriminant is -136, two complex roots

  2. Math

    Part 1: Suppose you divide a polynomial by a binomial. How do you know if the binomial is a factor of the polynomial? Create a sample problem that has a binomial which IS a factor of the polynomial being divided, and another

  3. pre cal

    Factor completely: 3x^2(4x2 + 1)^8 + 64x^4(4x2 + 1)^7.

  4. algebra

    Factor the trinomial below. Write each factor as a polynomial in descending order. Enter exponents using the caret ( ^ ). For example, you would enter x2 as x^2. 25x2 + 30x + 9

  1. calculus

    An open box is to be made from a square piece of cardboard, 32 inches on a side, by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below). Determine the function, V, in terms of

  2. algebra--1 question

    Suppose you divide a polynomial by a binomial. How do you know if the binomial is a factor of the polynomial? Create a sample problem that has a binomial which IS a factor of the polynomial being divided, and another problem that

  3. Algebra 2

    Examine the polynomial p(x)=6x^3+17x^2−24x−35. Use the Factor Theorem to identify which binomial is a factor of p(x). a.3x+5 b.2x+7 c.x−1 d.2x−7 I thought that 2x+7 was a factor of p(x) but I don't know and I am confused

  4. Algebra II

    Given polynomial f(X) and a factor of f(x), factor f(x) completely. F(x)= x^3-9x^2+8x+60; x+2

  1. Rational Zeros

    List all possible rational zeros for the polynomial below. Find all real zeros of the polynomial and factor f(x)=2x^4+19x^3+37x^2-55x-75

  2. Algebra 2 (Please help Ms. Sue!)

    Use synthetic division and the given factor to completely factor the polynomial. x^3-x^2-24x-36; (x-6) How do I do this?

  3. Algebra

    If 3 is a zero of the polynomial f(x), then which of the following is NOT necessarily true? A. (x – 3) is a factor of the polynomial f(x). B. 3 is a solution of the equation f(x) = 0. C. (3, 0) is an x-intercept for f. D. (0, 3)

  4. math-please help,need quickly

    solve the polynomial inequality and graph the solution set on a real num ber line. express the solution set in interval notation x^3+x^2+64x+64>0 please show work

You can view more similar questions or ask a new question.