Question

What is the completely factored form of f (x)=6x^3-13x^2-4x+15?

Answer 1

f(x) = 6x³ - 13x² - 4x + 15
f(x) = 6x³ - 19x² + 6x² + 15x - 19x + 15
f(x) = 6x² - 19x² + 15x + 6x² - 19x + 15
f(x) = x(6x²) - x(19x) + x(15) + 1(6x²) - 1(19x) + 1(15)
f(x) = x(6x² - 19x + 15) + 1(6x² - 19x + 15)
f(x) = (x + 1)(6x² - 19x + 15)
f(x) = (x + 1)(6x² - 10x - 9x + 15)
f(x) = (x + 1)(2x(3x) - 2x(5) - 3(3x) + 3(5))
f(x) = (x + 1)(2x(3x - 5) - 3(3x - 5))
f(x) = (x + 1)(2x - 3)(3x - 5)

= (x+1)(2x-3)(3x-5)

Answer 2

f(x)= (x+1)(2x-3)(3x-5)

Explanation:

f(x) = 6x³ - 13x² - 4x + 15

This could also be written as:

f(x) = 6x³ - 19x² + 6x² + 15x - 19x + 15

f(x) = 6x² - 19x² + 15x + 6x² - 19x + 15

f(x) = x(6x² - 19x + 15) + 1(6x² - 19x + 15)

f(x) = (x + 1)(6x² - 19x + 15)

f(x) = (x + 1)(6x² - 10x - 9x + 15)

f(x) = (x + 1)(2x(3x - 5) - 3(3x - 5))

f(x) = (x + 1)(2x - 3)(3x - 5)

f(x)= (x+1)(2x-3)(3x-5)