Question

Which of the following is a polynomial with roots 4, 6, and −7?

f(x) = x3 − 3x2 − 24x + 42
f(x) = x3 − 3x2 − 46x + 168
f(x) = x3 − 24x2 − 42x + 46
f(x) = x3 − 24x2 − 46x + 168

Answer 1

Try plugging in 4,6, and -7 into the x's 

Answer 2

option B

Explanation:

If any polynomial has roots 4, 6, and (-7) then x - 4, x- 6, and x+7 will be the 0 roots of the polynomial.

Then the polynomial can be written in the form of f(x) = (x-4) (x-6) (x+7)

Now we further solve it to get the simpler form of the polynomial.

f(x) = (x-6) [x² + 7x - 4x - 28]

= (x-6) [x² + 3x - 28 ]

= x³ + 3x² - 28x - 6x² - 18x + 168

= x³ - 3x² - 46x + 168

This polynomial matches with option B

So option B will be the option.