Question

Factor f(x)=4x^3 19x^2-149x 36 into linear factor given that -9 is a zero of f(x)

Answer 1

To factor the polynomial, perform synthetic division by the given zero -9 and then factor the resulting quadratic expression and we get is f(x) = (x + 9)(4x^2 - 19x + 4).

Step-by-step explanation:

To factor the given polynomial, we can use synthetic division to divide the polynomial by the zero -9. This will give us a quadratic expression, which we can then factor using other methods.

Performing synthetic division, we have:

-9 | 4 19 -149 36
-36 153 -4
4 -19 4 32

The remainder is 32, which means that the quadratic expression is f(x) = (x + 9)(4x^2 - 19x + 4).