Question

Show that x+5 is a factor of the polynomial f(x) = x³+ x²+ 3x +115​

Answer 1

Step-by-step explanation:

p(x)= -5

f(x) = $x^{3}$+$x^{2}$+3$x$+115

f(-5) = $(-5)^{3}$+$(-5)^{2}$+3(-5)+115

       = -125+25+(-15)+115

       = -125+25-15+115

       = 0

Therefore, x+5 is a factor of f(x) = $x^{3}$+$x^{2}$+3$x$+115.

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Answer 2

To find :

we need to show that x + 5 is a factor of given polynomial or not.

solution :

If x + 5 is a Factor of given polynomial then if we put the value of x in the given polynomial then value will came 0.

So, let's check :

• x + 5 = 0
• x = - 5

Now putting value of x in the given polynomial.

x³ + x² + 3x + 115

= (-5)³ + (-5)² + 3 × (-5) + 115

= -125 + 25 - 15 + 115

= - 140 + 140

= 0

Hence, we get 0

So, x + 5 is factor of given polynomial .

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