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Factor each of the following functions:

A)f(x)=x^4+3x^3-38x^2+24x+64

B)f(x)=6^4-19x^3-2x^2+44x-24

User Saaj
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2 votes

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:

User Norbert Bicsi
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