Tatiana7121idn
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Which of the following best describes the relationship between [tex]\((x+1)\)[/tex] and the polynomial [tex]\(-3x^3 - 2x^2 + 1\)[/tex]?

A. It is impossible to tell whether [tex]\((x+1)\)[/tex] is a factor.
B. [tex]\((x+1)\)[/tex] is not a factor.
C. [tex]\((x+1)\)[/tex] is a factor.

Sagot :

GinnyAnsweridn
To determine whether [tex]\((x+1)\)[/tex] is a factor of the polynomial [tex]\(-3x^3 - 2x^2 + 1\)[/tex], we can use the Factor Theorem. The Factor Theorem states that [tex]\((x - r)\)[/tex] is a factor of a polynomial [tex]\(P(x)\)[/tex] if and only if [tex]\(P(r) = 0\)[/tex].

In this case, we are dealing with [tex]\((x+1)\)[/tex], which can be rewritten as [tex]\((x - (-1))\)[/tex].

1. Step 1: Evaluate the polynomial at [tex]\(x = -1\)[/tex].

[tex]\[ P(x) = -3x^3 - 2x^2 + 1 \][/tex]

2. Step 2: Substitute [tex]\(x = -1\)[/tex] into the polynomial.

[tex]\[ P(-1) = -3(-1)^3 - 2(-1)^2 + 1 \][/tex]
[tex]\[ P(-1) = -3(-1) - 2(1) + 1 \][/tex]
[tex]\[ P(-1) = 3 - 2 + 1 \][/tex]
[tex]\[ P(-1) = 2 \][/tex]

3. Step 3: Check the result.

Since [tex]\(P(-1) = 2\)[/tex] and not 0, [tex]\((x+1)\)[/tex] is not a factor of the polynomial [tex]\(-3x^3 - 2x^2 + 1\)[/tex].

Therefore, the correct answer is:

B. [tex]\((x+1)\)[/tex] is not a factor.
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