Question

Is x+5 a factor of x³+3x²+15x+20​

Answer 1

Solution!!

The concept of Factor Theorem and Remainder Theorem has been used here.

Factor Theorem → When a polynomial f(x) is divided by x - a, the remainder is f(a). And, if the remainder f(a) is 0; x - a is a factor of the polynomial f(x).

Remainder Theorem → If f(x), a polynomial in x, is divided by (x - a), the remainder is f(a).

_______________________________

x + 5 = 0

x = -5

f(x) = x³ + 3x² + 15x + 20

f(-5) = (-5)³ + 3(-5)² + 15(-5) + 20

0 = -125 + 75 - 75 + 20

0 = -125 + 20

0 ≠ -105

So, we can say that x + 5 is not a factor of the polynomial.