Factor fx 4x3 19x2 101x 24 into linear factors given tha

Factor f(x) = 4x^3 + 19x^2 - 101x + 24 into linear factors given that - 8 is a zero of f(x). f(x) = 4x^3 + 19x^2 - 101x + 24 =

Solution

f(x) = 4x³ + 19x² - 101x + 24

x + 8 is a factor of f(x)

so, 4x³ + 19x² - 101x + 24 = (x + 8)(ax² + bx + c)

solving this gives, a = 4, b = - 13 and c = 3

therefore, the quotient will be: 4x² - 13x + 3

equate it to zero and solve this to find the other roots.

4x² - 13x + 3 = 0

the roots will be: x = 3 and x = 1/4

or 4x² - 13x + 3 = ( x - 3)(4x - 1)

therefore, 4x³ + 19x² - 101x + 24 = (x + 8)(x - 3)(4x - 1).