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Mashutka [201]
2 years ago
6

Is x + 1 a factor of

title="x^{4} +2x^{3} +2x^{2} -2x-3" alt="x^{4} +2x^{3} +2x^{2} -2x-3" align="absmiddle" class="latex-formula">?
Mathematics
2 answers:
JulsSmile [24]2 years ago
4 0
Yes x+1 is a factor of that
Svetllana [295]2 years ago
4 0

Answer:

Yes.

Step-by-step explanation:

We want to determine if (<em>x</em> + 1) is a factor of the polynomial:

x^4 + 2x^3 + 2x^2 - 2x -3

According to the Factor Theorem, if a binomial in the form (<em>x</em> - <em>a</em>) is a factor of a polynomial P(x), then P(a) must equal zero.

Our binomial factor is (<em>x</em> + 1) or (<em>x</em> - (-1)). Hence, <em>a</em> = -1.

Let our polynomial be P(x). Find P(-1):

\displaystyle\begin{aligned}  P(-1) &= (-1)^4 + 2(-1)^3 +2(-1)^2 -2(-1) -3 \\&=0\end{aligned}

Therefore, since the resulting value is indeed zero, (<em>x</em> + 1) is indeed a factor of the given polynomial.

In conclusion: yes.

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