Question

What is the factored form of the function f(x)=(x ² −13x+40)(x ² −2x−3)?

A) (x−5)(x−8)(x+1)(x−3)
B) (x−8)(x−5)(x+3)(x−1)
C) (x−3)(x+1)(x−5)(x−8)
D) (x+1)(x−3)(x−5)(x−8)

Answer 1

The factored form of the function f(x)=(x ² -13x+40)(x ² -2x-3) is determined by separately factoring each quadratic. After factoring, it is found to be (x+1)(x-3)(x-5)(x-8), which corresponds to option D.

Step-by-step explanation:

The factored form of the function f(x)=(x ² -13x+40)(x ² -2x-3) can be found by factoring each quadratic equation separately.

For the first quadratic equation, x ² -13x+40, we look for two numbers that multiply to 40 and add up to -13. These numbers are -5 and -8, so the factored form of this quadratic is (x-5)(x-8).

For the second quadratic equation, x ² -2x-3, we find two numbers that multiply to -3 and add up to -2. These numbers are -3 and +1, giving us the factored form (x+1)(x-3).

Putting it all together, the factored form of the given function is therefore option D: (x+1)(x-3)(x-5)(x-8).