Question

Determine whether the binomial (x-4) is a factor of the polynomial p(x) = 5x³ - 20x² - 5x+ 20-

Answer 1

`x - 4 = 0 \\ x = 4 \\`

substitute value of x in the function to see if it equals to zero , if not it won't be a factor of the function

`5 {x}^(3) - 20 {x}^(2) - 5x + 20 = 0 \\ 5(4) ^(3) - 20( {4})^(2) - 5(4) + 20 = 0 \\ 5(64) - 20(16) - 20 + 20 = 0 \\ 320 - 320 - 20 + 20 = 0 \\ 0 = 0`

so (x-4) is a factor for the function

Answer 2

Explanation:

IF x-4 is a factor, then putting in x = + 4 will make the polynomial = 0

5 ( 4^3) - 20 (4^2) - 5(4) + 20 = 0 Yes...it is a factor