The remainder theorem is a useful tool in algebra to find the remainder when a polynomial is divided by a linear divisor of the form $x - a$. The remainder is the value of the polynomial at .
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If $f(x) = x^2 - 5x + 6$ and is divided by $x - 2$, apply the remainder theorem to find that the remainder is .
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If the remainder is 0 when $f(x)$ is divided by $x - 3$, it indicates that $x - 3$ is a(n) of $f(x)$.
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To apply the remainder theorem to the polynomial $f(x) = 2x^3 + 3x^2 - x + 5$ divided by $x - 2$, you calculate the value of $f(2)$, which is .
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To find the roots of the equation $x^2 + 4x + 4 = 0$, resolve into factors by recognizing it as a perfect square: $(x + 2)^2 = 0$, so the root is .