Respuesta :

Let's try (x+5) first. According to the Remainder Theorem, if (x+5) is a factor of the polynomial, the remainder is zero. 

when x+5=0, x=-5
use synthetic division:

-5 I  1    7    11     5
    I        -5    -10   -5
     ----------------------
        1    2     1      0
the remainder is 0, so (x+5) is a factor:
the result is (x+5)(x²+2x+1)
factor again: (x+5)(x+1)(x+1) is the final answer. 
    

Completely factor p(x) = x 3 + 7x 2 + 11x + 5 are (x+5)(x+1)(x+1).

What is synthetic division?

A more straightforward approach to dividing a polynomial of the first degree by another polynomial of the same degree involves only writing down the coefficients of the various powers of the variable and changing the sign of the constant term in the divisor to substitute additions for the more common subtractions.

How to find the factor of p(x)?

The given function is p(x) = x³ + 7x² + 11x + 5.

We have to find factors in this function.

First, find the value of a function on x=-5.

Use synthetic division:

-5 I  1    7    11     5

   I        -5    -10   -5

    ----------------------

       1    2     1      0

the remainder is 0.

So (x+5) is a factor

therefore, p(x) = (x+5)(x²+2x+1)

                        = (x+5)(x+1)²

Hence factor of p(x) are (x+5)(x+1)(x+1).

Learn more about synthetic division here: https://brainly.com/question/24662212

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