Question

Factor each of the following functions:

Show your work

A)f(x)=x^4+3x^3-38x^2+24x+64 B)f(x)=6^4-19x^3-2x^2+44x-24

Answer 1

A) To factor the function f(x) = x^4 + 3x^3 - 38x^2 + 24x + 64, we can use the technique of grouping and factor by grouping:

Step 1: Group the terms in pairs:

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

Step 2: Factor out the common terms from each group:

x^3(x + 3) - 2x(19x - 12) + 64

Step 3: Factor out the common factors from the entire expression:

x^3(x + 3) - 2x(19x - 12) + 64

So, the factored form of f(x) is:

f(x) = x^3(x + 3) - 2x(19x - 12) + 64

B) To factor the function f(x) = 6x^4 - 19x^3 - 2x^2 + 44x - 24, we can use the technique of grouping and factor by grouping:

Step 1: Group the terms in pairs:

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

Step 2: Factor out the common terms from each group:

x^3(6x - 19) - 2x(x - 22) - 24

Step 3: Factor out the common factors from the entire expression:

x^3(6x - 19) - 2x(x - 22) - 24

So, the factored form of f(x) is:

f(x) = x^3(6x - 19) - 2x(x - 22) - 24