Use the Factor Theorem to determine whether the first polynomial is a factor of the second polynomial.
-$$x + 3 ; 7 x ^ { 4 } + 22 x ^ { 3 } - 3 x ^ { 2 } + x + 4$$

Question

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The Factor Theorem states that a polynomial $f(x)$ has a factor $x - c$ if and only if $f(c) = 0$. Substituting $x = -3$ into the given polynomial $7x^4 + 22x^3 - 3x^2 + x + 4$, we get $7(-3)^4 + 22(-3)^3 - 3(-3)^2 + (-3) + 4$, which simplifies to $567 - 198 - 27 - 3 + 4$, or $343$, not $0$. Therefore, $x + 3$ is not a factor of the given polynomial.

Use the Factor Theorem to Determine Whether the First Polynomial x+3;7x4+22x3−3x2+x+4x + 3 ; 7 x ^ { 4 } + 22 x ^ { 3 } - 3 x ^ { 2 } + x + 4x+3;7x4+22x3−3x2+x+4

Use the Factor Theorem to Determine Whether the First Polynomial $x + 3 ; 7 x ^ { 4 } + 22 x ^ { 3 } - 3 x ^ { 2 } + x + 4$