What is a factor of f(x) = 5x³ + 24x² - 75x + 14?

Solution:

The function given is

f(x) = 5x³ + 24x² - 75x + 14

Let us substitute x = 2  in the given polynomial,

we get,

f(2) =  5(2)³ + 24(2)² - (75 x 2) + 14.

f(2) = 40 + 96 - 150 + 14

f(2) = 0

Hence x - 2 is a factor of the given polynomial.

The quotient here is 5x² + 34x - 7

By splitting the middle term

= 5x² - 1x + 35x - 7

Taking the common terms out

= x(5x - 1) + 7(5x - 1)

= (5x - 1)(x + 7)

Therefore, the factors for f(x) = 5x³ + 24x² - 75x + 14 are (5x - 1)(x + 7)(x - 2).

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What is a factor of f(x) = 5x³ + 24x² - 75x + 14?

Summary:

The factors of f(x) = 5x³ + 24x² - 75x + 14 are (5x - 1)(x + 7)(x - 2).