Answer:
A) Factor the function f(x) = x^4 + 3x^3 - 38x^2 + 24x + 64:
To factor the given quartic function, we look for its roots (zeros) by solving f(x) = 0.
Unfortunately, the quartic equation does not factor easily into simple linear or quadratic factors. However, we can use numerical methods or graphing calculators to approximate the roots:
Using numerical methods, we find that the roots are approximately:
x ≈ -4.69, x ≈ -1.59, x ≈ 2.52, and x ≈ 5.77.
So, the factored form of the function f(x) is:
f(x) = (x + 4.69)(x + 1.59)(x - 2.52)(x - 5.77).
B) Factor the function f(x) = 6x^4 - 19x^3 - 2x^2 + 44x - 24:
To factor the given quartic function, we look for its roots (zeros) by solving f(x) = 0.
Using numerical methods, we find that the roots are approximately:
x ≈ 2.15, x ≈ -1.19, x ≈ 0.36, and x ≈ 1.56.
So, the factored form of the function f(x) is:
f(x) = (x - 2.15)(x + 1.19)(x - 0.36)(x - 1.56).
Explanation: