Question

show that x-5 is a factor of the polynomial f(x)=x^3+x^2+3x+115.

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Answer 1

Answer:

(x - 5) is not the factor of the polynomial x³ + x² + 3x + 115.

Step-by-step explanation:

To check : (x - 5) is a factor of polynomial (x³ + x² + 3x + 115.)

To show the above, simply plug out the value of x from (x - 5), and then substitute it in the polynomial.

If the result comes 0, it means that (x - 5) is a factor. Here we go;

• x - 5 = 0
• x = 5

Putting the value of x in the above polynomial.

⇒ x³ + x² + 3x + 115

⇒ 5³ + 5² + 3 * 5 + 115

⇒ 125 + 25 + 15 + 115

⇒ 280

Since remainder is not zero. Hence, (x - 5) is not the factor of the polynomial (x³ + x² + 3x + 115).

Answer 2

f(x) = x³ + x² + 3x + 115

x - 5 is the factor of the above polynomial.

____________ [GIVEN]

=> x - 5 = 0

=> x = 5

Put the value of x in above polynomial. If the remainder came zero (0) then x - 5 is the factor of the polynomial x³ + x² + 3x + 115

=> (5)³ + (5)² + 3(5) + 115

=> 125 + 25 + 15 + 115

=> 280

Then remainder came is 280 which is not 0.

_____________________________

So, x - 5 is not a factor of the polynomial x³ + x² + 3x + 115

___________ [ANSWER]